Question

GPT: \(2x^2+\left(14-2\sqrt{x^2+8x}\right)x+8x-14\sqrt{x^2+8x}+24=0\)

Answer 1

Lời giải:

ĐKXĐ:............

PT \(\Leftrightarrow 2x^2+14x-2x\sqrt{x^2+8x}+8x-14\sqrt{x^2+8x}+24=0\)

\(\Leftrightarrow (x^2+8x)+(x^2+14x+49)-2(x+7)\sqrt{x^2+8x}-25=0\)

\(\Leftrightarrow (x^2+8x)+(x+7)^2-2(x+7)\sqrt{x^2+8x}-25=0\)

\(\Leftrightarrow (\sqrt{x^2+8x}-x-7)^2-25=0\)

\(\Leftrightarrow (\sqrt{x^2+8x}-x-12)(\sqrt{x^2+8x}-x-2)=0\)

Nếu \(\sqrt{x^2+8x}-x-12=0\)

\(\Leftrightarrow \sqrt{x^2+8x}=x+12\Rightarrow \left\{\begin{matrix} x+12\geq 0\\ x^2+8x=(x+12)^2\end{matrix}\right.\)

\(\Rightarrow x=-9\) (thỏa mãn)

Nếu \(\sqrt{x^2+8x}-x-2=0\Leftrightarrow \sqrt{x^2+8x}=x+2\Rightarrow \left\{\begin{matrix} x+2\geq 0\\ x^2+8x=(x+2)^2\end{matrix}\right.\Rightarrow x=1\) (thỏa mãn)

Vậy.........