Question

resolva a equação √5x-9=x-1​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{\sqrt{5x - 9} = x - 1}$

$\mathsf{(\sqrt{5x - 9})^2 = (x - 1)^2}$

$\mathsf{5x - 9 = x^2 - 2x + 1}$

$\mathsf{x^2 - 7x + 10 = 0}\rightarrow\begin{cases}\mathsf{a = 1}\\\mathsf{b = -7}\\\mathsf{c = 10}\end{cases}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-7)^2 - 4.1.10}$

$\mathsf{\Delta = 49 - 40}$

$\mathsf{\Delta = 9}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{7 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{7 + 3}{2} = \dfrac{10}{2} = 5}\\\\\mathsf{x'' = \dfrac{7 - 3}{2} = \dfrac{4}{2} = 2}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{\:5\:;2\:\}}}}$

Answer 2

Resposta:

$x = \frac{8}{\sqrt{5-1} } = \\\\x = 6,472....$

Explicação passo-a-passo: