Question

[:vvv]

Giải pt: 

\(\sqrt{x-1}+\sqrt{x+7}+x^2-3x-2=0\)

Answer 1

[Nguyễn Việt Lâm]

ĐKXĐ: \(x\ge1\)

\(\left(\sqrt{x-1}-1\right)+\left(\sqrt{x+7}-3\right)+\left(x^2-3x+2\right)=0\)

\(\Leftrightarrow\dfrac{x-2}{\sqrt{x-1}+1}+\dfrac{x-2}{\sqrt{x+7}+3}+\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(\dfrac{1}{\sqrt{x-1}+1}+\dfrac{1}{\sqrt{x+7}+3}+x-1\right)=0\)

\(\Leftrightarrow x-2=0\)