Question

Resolva equações racionais, com verificação


b) √7x-1 = √5x+1

Answer 1

$\large\textsf{Vamos L\'a:}$

$\boxed{\large\textbf{Equa\c{c}\~oes Irracionais}}$

$\mathsf{b) \ \ \sqrt{7x-1} = \sqrt{5x+1}}$

$\mathsf{\sqrt{7x-1} = \sqrt{5x+1}}$

Eleva-se os dois lados da igualdade ao quadrado, para eliminar as raízes.

$\mathsf{(\diagup\!\!\!\!\sqrt{7x-1})^\diagup\!\!\!^2 = (\diagup\!\!\!\!\sqrt{5x+1})^\diagup\!\!\!^2}$

$\mathsf{7x-1 = 5x+1}$
$\mathsf{7x-1-5x = 1}$
$\mathsf{2x = 1+1}$
$\mathsf{2x = 2}$
$\mathsf{x = 2/2}$

$\boxed{\large\mathsf{x = 1}}$

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$\large\texttt{VERIFICA\c{C}\~AO:}$

$\mathsf{\sqrt{7x-1} = \sqrt{5x+1}}$
$\mathsf{\sqrt{7*(1)-1} = \sqrt{5*(1)+1}}$
$\mathsf{\sqrt{7-1} = \sqrt{5+1}}$

$\sqrt{6} = \sqrt{6}}$   ✔

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Bons Estudos!!!