Question

Giải phương trình : 2(3x+5). \(\sqrt{x^2+9}\)= 3\(x^2\)+ 2x + 30

Answer 1

\(2\left(3x+5\right)\sqrt{x^2+9}=3x^2+2x+30\)

\(\Leftrightarrow\sqrt{x^2+9}=\frac{3x^2+2x+30}{2\left(3x+5\right)}\)

\(\Leftrightarrow\sqrt{x^2+9}-3=\frac{3x^2+2x+30}{2\left(3x+5\right)}-3\)

\(\Leftrightarrow\frac{x^2+9-9}{\sqrt{x^2+9}+3}-\frac{3x^2-16x}{6x+10}=0\)

\(\Leftrightarrow\frac{x^2}{\sqrt{x^2+9}+3}-\frac{x\left(3x-16\right)}{6x+10}=0\)

\(\Leftrightarrow x\left(\frac{x}{\sqrt{x^2+9}+3}-\frac{3x-16}{6x+10}\right)=0\)

Pt trong ngoặc vô nghiệm suy ra x=0