Question

Giải phương trình: \(\left(x+3\sqrt{x}+2\right)\left(x+9\sqrt{x}+18\right)=168x\)

Answer 1

\(\Leftrightarrow\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)\left(\sqrt{x}+6\right)=168x\\ \Leftrightarrow\left(x+7\sqrt{x}+6\right)\left(x+5\sqrt{x}+6\right)-168x=0\\ \Leftrightarrow\left(x+6\sqrt{x}+6\right)^2-\left(13\sqrt{x}\right)^2=0\\ \left(x-7\sqrt{x}+6\right)\left(x+19\sqrt{x}+6\right)=0 \\ \left(\sqrt{x}-1\right)\left(\sqrt{x}-6\right)=0\)