i love you
hãy trả lời câu hỏi của nàng tiên xinh đẹp
hình như là gpt :v
\(5\sqrt{x^2+9}+2\sqrt{x}=\frac{x^2}{2}+\frac{x}{2}+19\)
ĐK:\(x\ge0\)
\(pt\Leftrightarrow5\sqrt{x^2+9}-25+2\sqrt{x}-4=\frac{x^2}{2}+\frac{x}{2}-10\)
\(\Leftrightarrow\frac{25\left(x^2+9\right)-625}{5\sqrt{x^2+9}+25}+\frac{4x-16}{2\sqrt{x}+4}=\frac{x^2+x-20}{2}\)
\(\Leftrightarrow\frac{25x^2-400}{5\sqrt{x^2+9}+25}+\frac{4x-16}{2\sqrt{x}+4}-\frac{x^2+x-20}{2}=0\)
\(\Leftrightarrow\frac{25\left(x-4\right)\left(x+4\right)}{5\sqrt{x^2+9}+25}+\frac{4\left(x-4\right)}{2\sqrt{x}+4}-\frac{\left(x-4\right)\left(x+5\right)}{2}=0\)
\(\Leftrightarrow\left(x-4\right)\left(\frac{25\left(x+4\right)}{5\sqrt{x^2+9}+25}+\frac{4}{2\sqrt{x}+4}-\frac{\left(x+5\right)}{2}\right)=0\)
Suy ra x=4
