Question

Giải phương trình:

\(x-\sqrt{x-15}=17\)

Answer 1

ĐK:x\(\ge17\)

Ta có \(x-\sqrt{x-15}=17\Leftrightarrow x-17=\sqrt{x-15}\Leftrightarrow\left(x-17\right)^2=\left(\sqrt{x-15}\right)^2\Leftrightarrow x^2-34x+289=x-15\Leftrightarrow x^2-35x+304=0\Leftrightarrow x^2-19x-16x+304=0\Leftrightarrow x\left(x-19\right)-16\left(x-19\right)=0\Leftrightarrow\left(x-19\right)\left(x-16\right)=0\Leftrightarrow\)\(\left[{}\begin{matrix}x-19=0\\x-16=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=19\left(tm\right)\\x=16\left(ktm\right)\end{matrix}\right.\)

Vậy S={19}