RACIONALIZAÇÃO DE DENOMINADORES
Qual dos números, ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t8lqBIdkTSghx1teQgLBET__zz4bZ2Rz1mBb1yR8zXYoOXd7nXmydpbWWqOtuqcCnMeHZ5nerd862hFTjKP802TNT6EbeoJgs0Z_E031JlsyDmo_JQNEHdDsGPle2oxcMTiI22OzGy-PHr7KYm3UZcGwSZd2ytIIG2SvmeO83IMyee4k8HxjgCE_Ya9DDQlnTW7hf_=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sGHeFWWp6r3lhjvTtaoWJ-NnjJv6CDQY_FrcXqQIndDop7eyfG3VE2riVXzrLpGgk6IA1pG5X7Ea0PGCRY1hsKhFWv5j1kPHRqAzvCp9ie_pp2TZoLie4N4bh8VBzfOHHBtrKRGausYobLKIZLW-Hz-WJyBXJIDAGwkWQ8hMQtPt5JbCUK-jZfa-igSwYHumE96A=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_szmhWXuOFmHonLnbz-rTaJwMI5pIAf20U1dwVr-J1JjPp00aJzlajn_6cg1viVI-bFLLSZsc5l5CquMCVCjkrPmk_U69NB7gT5hNceQqfUQtn1WSU2yt8tzEPUjK6M-2voS0zA6MEejo0cxkokBNlr1cyGIeL7GHqPvwAhY5FrEDmVtFkNyWUCiElfF8Kt3oT7UsE=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
e ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uoUkpi3z_CPTRJGEJHAH3R9SR8G3tNtoiMTWqvOLaAQB23nxPGwIhiYO5fLuxlNNt1MJteIuagVjXQFY7Piy3fDksKlRzsKizKZc-oZuL3ohU9vMFEhMnwVVf8hXLUdLiggFES9FwBGMyzkiqQdDkvMOaozz5ws4NbFWjsQfeDt7EQP2jp0F7TYEJYJGJw3H0Ogpfw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uj0tuw9czBdRa6_63KrdLzz2hsJJID5mfS4wkHfoacBpxVWvi-eNTsOx9hl7_lxyV_NlWYS_oeEHMAUPHcBF6jUfrq0mtNIs1LhcrEyIjkq9-9mGiZ4jvKDbjc59AAAN4JBtvaz1EJ95SjJFafd53-MHtMWBpLJ3ra5mIkEsrUZ-Li_MKNfilVu2wETU0wLcK_XK0=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_svL-Xt1veQvE9vUMWHRBfcDHXsGnjOWfgmGbJ-eUQ9YdR4Qfic5oV9FmF6MqJw_ftNSUOxpVgBrbFFgDFTfZnK7h0y7V6AGwStKMto7PXUH0c3iawW9oZ5C5LvakyL4Kix0v5FYujUnov-8e-EMWVUbiM0gvCUsrM2tmQ8EWldTt-t5jAPJNY9bEGI-Fv0nlG29A=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
, é maior?
Determinar mentalmente um valor aproximado de ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s3rIef7klvgjJ2BcIClXVzH8e2f63Oa7qJ8IAsmv4CQIT-fVLA2OjYev7mpSYH7Rh2q1f-baeP51LvBclQOFotLnXL6VNodHinX559cj2rCn8pWpm-9ugsTiO9M5Gemi6DmU5gw7gO2Y_pzmuYlQ04dH09gqCMnbJmtHxE6b8hVtntcenp4cBP_FPZr0pMKSNwo5ho=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uj0566q0wotSiyK81ogJlvljTfnIPxELaEkd1NafzuE5JF_W4wwAXMsFocxD7hz7sHb4h7CCgNXman8C0XwdQDWEuFTfYiE-Ek30Q8Qv5Ex0O0xH-RcMYlEQEyI0uPTlu0nVJjCyXqpbhbHOCzUAjOARZMk9-M0sQbezdyIhfwRfUGHfipt0_233yOX2aLEvn-Ks0=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vhWLrqK745SN_iU4g5JWSTh3DfGKOrsah-0WrwSDS-pZWN1msowx0dJZkTAGP8q8ILdV38l6Ljj4xMbECgOGYoH4DcXQS4fG_ABGTna1HFy0pvY5A-5OCd7bdIo2vFQCtbkmE0AMiCJUlKTFZvuiJ-Aq_mfUGzX-cXhJlM9GW6-s2KVQSoylCCRWafEJ-AjNngnjQ=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
é relativamente fácil, pois sabemos que ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t-6IefsfljlV-mQwXZKHxldfwcwLO9zx4glI8Dm1Mz15lmiseB8MYRlsC0_SZ5zV0y609U4u3O694hANLX8bwITRTlSLGxLnTz1xUulEyspGYm4Y6PtLuQ7B1jRiDgKb_Qs7DRmfJbk8HdFwq11xqnkZFcutdSpt5wY8ejWTQDzX6moZ33v7E-PtuCOZI4TcYfX60=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vTZ8q3ml_U3Fn7Fxzp8dy4rR9vXK_KKgtLrLGiFVXT9nz1DguFHF-CcZ3F1Wm8Hy_s7niESxPQhL3kxMGu75nyub9g6Fz3yk37Miwg3zOLe_DogALbjDGDYczzyMyya1WxksGp0u22SHOP5ecac2a4pcJUTLyYrls4xNGPLXOQb5eG7TEqHMCqRj2nIyW6t8D9UA=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_us2s_O2ymx_rCfwdwnVGVcJlOPC1_CpsHIwY7xbo3Nt1dBhXbHsWHxiX4ECXZH7kOz-iFfjXhK0fM5ONNeRT2-Fd576swlfl-1BPBGiQPWPGDqsrKJ4H7KACyAkBgfXGyZHtRPdsFl-wX_rHmyN4a8g50-uDgN0PLT7zwgFJQC6SEep33vp399zrl73cVuTbRuaq8=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
é um valor aproximado de ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uqWHkMzA1kyqzeduyz9fWe9s6icfXKXK7Fi77eLHUNYjjOaPjUabQJCWhyemZ1QoK0vIm6-Q_sO6DDpovSBXte5UmrxenIv_cVXl-0exurtYytmVpudSSqTrW_zk_6km8Y3QJgEm5lTCg0UZ8gzd8nq7JZqmWutkq01mM3h_eFE4ZCgn96rDNMEYR6k0qDSq4jyK6w=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sThZEYoLJ_MHojCoO9be6Le1vqZ56wMs9rEDhdKJkAqpr6uXSUFJzj05uGvBqbm2ryNcDPMSfJ5qAM2YSK8FKFOHU-MSshBdQh8y7RGfXQg9WN-g8CCQqUXMAmTVvUwws7T8lvcB2I4vehMNoQvphvgiffAwRejbBFMiAsI314i2KrbU4G8WMR9-2nb7vXfxBXE_k=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sDfUb9tMlzMCUy9QcKsRU6N23ozzyl2B5NAJf1qjW_HoKW_isiq6-Pvqo-_4XaMTnlaikKENZmRj92cq17wANDlha_cARJ5zF0AhAF0MlLbOyt-ZRKbzUfOtXq6Tu_B0Q6uBksH2tJbto9XauTVg9qKhVrnoMNt4jVcPziuUrFeBPbjSxhtCVOWpgG052lJ5bYVXs=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
, às décimas. Mas, determinar mentalmente um valor aproximado de ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_umBuixhMfbXEzxsezwkWv3K2X9fQmtbGTksD3MedqTX84q2rhKN965nFR83lH9AsJPfaU4DL3q3QcovOix6YaWolCtpE5PLtSlA1JF5Lx1GWKAzZ0MY5Zs4CpQVhmUcFmlfxgSpNPFbsaWOjbTiXQMoqUgCO_i66-dVQ5QKnCXDrMbVhaQcDDSECHhSN9V09xLTUH0=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vfV8Y8n8ANYO70zGu3hrXyZvVHljEfXlRSIPw-nJfLa9JRjdllfaRBYpxs4JoO5T6AlDpCY2KhK9tm0oLLQW50mydKYGffq3Q_j4a_chkXb6olFMHC6ofvY9kjSB4M7KmwBPfMApAnqp2bOgX48pMSIKmq4nem6r0M2kUVOo4THrhEIDxzq5VH6PIK2H-LB2qAXYc=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t8J15sdBaI488nMGN_Cg82GNbtiXnNH_ISPFjwZwhLRNYEVXGbbXEIqqj-V6UaaTPsQbC-Q_6leDKTyGAF0Oqi3XfcsKIDwe96Tl9c_jt5b9W2XLWrVE4rqW1y69c0iaWu0kZLc4loJumIQ1cJBJtKlydkn0CD7x63rRnVUfb7DWEvkR4HoGpuGQPKbuBFSqVpog=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
já não é tarefa fácil.
Bem... quem diria que as fracções são equivalentes?! Com efeito: ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v_QAjhO0aBFsJSi0UHvweokDLNBb0b6CXVU2-m7LHbjmw-4DXssObCrQMeKAv6dB3SFLROWmRuLuJHTVQqhWcqGTc5nUYg7wglRTJ174HLjaNlkBx1X3BUoWKStPg7RZAIEnNwInIKXwmIze84Bk2vCEnyS_6fHhHQCQjPE63A5hKQj9-xvX9hPoFA4dE0EtjvuB7i=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tkLBtkhQ9A_CAmZUEkV9FWM7mny2kgUpXk6jN9lVZ4WWellmoZ2SyMjqFv8uFHlu0KXfzQUEnDQrdICcP8qgWD_1Z3UJafqFTN2Vuvt46QytS1f984X097XfW64-TS7QBcaf8Dc8XrWaU50yz9O0rbFP1rDssC9iS0XWJv0ZQPhhR7oyuTbG8syqdQQhO1T_yJGNc=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vdnn08GFC_nLtODluPvcUv8kwwdk2sSL-ecrXKye67E_VM237bFFEiKX5dXswO4Q53qU-bGoztaxN6Xh2FpmNuDapiA2dYaUVS_gLYlE0n3zrzdPYB1DIwRLjITQJnfxEMurxUhWIZ0rYSfPI4FKrAWeU7LEx60-XMwycxfiUt5kWpUv5VDUi_frPDlqqlojIkf2I=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
.
O denominador da fracção ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vycXxCRTo9KxlpgAa9upp-QqPULDUKk4jlVmuTXEOz4M6SFo_zwDxQq88Ykem7S1a8u4WYoZfocr2Na6lt2hMS8igplcVrTNIo7WlxqTXr2rweCZD4nXKCbnuRyjlNUrAhTHngyVXY53VN-HyO3GPm3ZvunRrx4rTm7tpOkg7rPAx2tht2FRTzHMWZ9gq6y0-_z64=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v42t-xGZPAVZeV9ZRlK1OzgZE9fvYcTaMUHOcLmHkKJ9Y2T9yzNxubah3Gnz0IB15RCa3YoJR_fxMHq-IePpMbFvu3BddKdXGNJ8wVOs5cAMOZYsv0SgSG24VvFltWHusiIi49qkk1Fz2hBymIezFPIuNu3euZDK3KqSqqKla_0d1vHJwjYeoDIeQYhF6A8HD6d6o=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ui8gKYszyevrKPzbXaF1k1Lh8An2rMb8qdU2VhP4Xd7_SwJXFrHmiLYKxWMTTZNenqaenRh8OoLwUFPgwBmigXgoUfWNo9HCisqgdQZd7X9ey9bshfox4UaWY2p7LsluYOBfIS_CICXuflBue-BuPbR0SOa7RI5e41yfp1d96Ev2thi1ghSmhmutQK-6U6ovOjeA=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
é um número irracional, enquanto o denominador de ![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uAfsLthTYlZaPvxEsOtXIeazI3p57PEnWfHvbCQaV0m3po3z-T6PDO3N_Kb4JEHXQAkqnOpBoFpU19J7BmMdGsSUfkSG9sLavyUe7sGSVYcLlAWtOjOseWZ7N8w5OB2mJRB-1DRCEuKiwmilOUoY-D9McFyVqeSf-AErVsFuURLz330UHtpcfjy4_vos8TO9_XrVxG=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u4ZBtZK900BmruZPszeg25QBAa9GkED1J2EBeMJO0M_G85DNuizcTkM5bUy8T35Zo2PvvS3jkKoGfYgPATUUvMglbXN5jUSBm0xDlwFW5zGCRaz-GrcNiRxVDrBwRdjBbLWqGMkDcA6_ovqj42LF-OnSbxvBv46zYDwI62wy1Wgu2DvIf_7AVpLPBulfkBEsObvKI=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s0F6Hks25-HrYKSV5uKX_L7u38kb46o_XlOnvi_CNFfaFa3FS2FuzqQxHW2vtsHH8OJk1E6oZFSCtBGLpO93xEGYJwP8xRmhwBG2nIlJRTg_s2zyhHPOIOfzFH6cAKsrGs40p6ajXnCXnPldisK8P9s3CkU54Z9kdiv691sW2iFt_h-Yk3Sa_YCf2JuIm0W2iM55s=s0-d)
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_swG1zq542GjrDJStmgdeqQ1xszdJiSYBmY0zld2zfZBbm4E4KMajf-gxTon0J83nD75GQBu9bwDUdz04vIObxPdYkKru-AARKdwNP_jDXp3zZ52W__qyF-Ep61DEFsAr_QXGRRyM-XNVgTdqcXN-UpJFVK1yi6mP7RCiJma_Nepfx_E3aUkcB0iSvS1UuCAtFw=s0-d)
é um número racional. Diz‑se que racionalizámos o denominador da primeira fracção. Esta é a transformação que, por norma, se aplica a todos os resultados em forma de fracção com denominador irracional.
Exemplos
Equações do 2º grau
Equação Completa do segundo grau
Uma equação do segundo grau é completa, se todos os coeficientes a, b e c são diferentes de zero.
Exemplos:
- 2 x² + 7x + 5 = 0
- 3 x² + x + 2 = 0
Equação incompleta do segundo grau
Uma equação do segundo grau é incompleta se b=0 ou c=0 ou b=c=0. Na equação incompleta o coeficiente a é diferente de zero.
Exemplos:
- 4 x² + 6x = 0
- 3 x² + 9 = 0
- 2 x² = 0
Resolução de equações incompletas do 2o. grau
Equações do tipo ax²=0: Basta dividir toda a equação por a para obter:
x² = 0
significando que a equação possui duas raízes iguais a zero.
Equações do tipo ax²+c=0: Novamente dividimos toda a equação por a e passamos o termo constante para o segundo membro para obter:
x² = -c/a.
Autores: Pattricia ,Naiara, Ándre , Lucas G.
Se -c/a for positivo, a equação terá duas raízes com o mesmo valor absoluto (módulo) mas de sinais contrários.
Equações do tipo ax²+bx=0: Neste caso, fatoramos a equação para obter:
x (ax + b) = 0
e a equação terá duas raízes:
x' = 0 ou x" = -b/a
Exemplos gerais
- 4x²=0 tem duas raízes nulas.
- 4x²-8=0 tem duas raízes: x'=R[2], x"= -R[2]
- 4x²+5=0 não tem raízes reais.
- 4x²-12x=0 tem duas raízes reais: x'=3, x"=0
Exercícios: Resolver as equações incompletas do segundo grau.
- x² + 6x = 0
- 2 x² = 0
- 3 x² + 7 = 0
- 2 x² + 5 = 0
- 10 x² = 0
- 9 x² - 18 = 0
Autores: Pattricia ,Naiara, Ándre , Lucas G.