Question

\(\sqrt{x}\text{+}\sqrt{x\text{ -}5}\text{+}\sqrt{x\text{+}7}=9\)9  giải pt 

Answer 1

\(\sqrt{x}+\sqrt{x-5}+\sqrt{x+7}=9\)

Đk: \(x\ge5\)

\(\Leftrightarrow\sqrt{x}-3+\sqrt{x-5}-2+\sqrt{x+7}-4=0\)

\(\Leftrightarrow\frac{x-9}{\sqrt{x}+3}+\frac{x-5-4}{\sqrt{x-5}+2}+\frac{x+7-16}{\sqrt{x+7}+4}=0\)

\(\Leftrightarrow\frac{x-9}{\sqrt{x}+3}+\frac{x-9}{\sqrt{x-5}+2}+\frac{x-9}{\sqrt{x+7}+4}=0\)

\(\Leftrightarrow\left(x-9\right)\left(\frac{1}{\sqrt{x}+3}+\frac{1}{\sqrt{x-5}+2}+\frac{1}{\sqrt{x+7}+4}\right)=0\)

Dễ thấy: \(\frac{1}{\sqrt{x}+3}+\frac{1}{\sqrt{x-5}+2}+\frac{1}{\sqrt{x+7}+4}>0\)

\(\Rightarrow x-9=0\Rightarrow x=9\) (thỏa)

Answer 2

=9 chứ k phải 99