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IgorA88
@IgorA88
January 2020
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Racionalize o denominador :
3/(√3 - √2 + 1 )
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JuarezJr
Verified answer
3
⇒ fator racionalizante (√3 - √2) - 1
√3 - √2 + 1
3
·
[(√3 - √2) - 1]
=
3[(√3 - √2) - 1]
=
3√3 - 3√2 - 3
=
3√3 - 3√2 - 3
[(√3 - √2) + 1] [(√3 - √2) - 1] [(√3 - √2)² - 1] 3 - 2√6 + 4 - 1 6 - 2√6
Agora, aplicamos o fator racionalizante 6 + 2√6
(3√3 - 3√2 - 3)
·
(6 + 2√6)
=
(3√3 - 3√2 - 3)(6 + 2√6)
=
6(3√3 - 2√3 - √6 - 3)
=
(6 - 2√6) (6 + 2√6) 36 - 4√36 36 - 24
=
6(√3 - √6 - 3)
=
√3 - √6 - 3
[resposta]
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Verified answer
3 ⇒ fator racionalizante (√3 - √2) - 1√3 - √2 + 1
3 · [(√3 - √2) - 1] = 3[(√3 - √2) - 1] = 3√3 - 3√2 - 3 = 3√3 - 3√2 - 3
[(√3 - √2) + 1] [(√3 - √2) - 1] [(√3 - √2)² - 1] 3 - 2√6 + 4 - 1 6 - 2√6
Agora, aplicamos o fator racionalizante 6 + 2√6
(3√3 - 3√2 - 3) · (6 + 2√6) = (3√3 - 3√2 - 3)(6 + 2√6) = 6(3√3 - 2√3 - √6 - 3) =
(6 - 2√6) (6 + 2√6) 36 - 4√36 36 - 24
= 6(√3 - √6 - 3) = √3 - √6 - 3 [resposta]
12 2