Question

giải phương trình (2x+3)(x+2)^2(2x+5)=3

Answer 1

\(\left(2x+3\right)\left(x+2\right)^2\left(2x+5\right)=3\)

\(\left(2x+3\right)\left(2x+5\right)\left(x^2+4x+4\right)=3\)

\(\left(4x^2+16x+15\right)\left(x^2+4x+4\right)=3\)

đặt \(\left(x^2+4x+4\right)=t\ge0\)

\(\left(4t-1\right)t=3\Leftrightarrow4t^2-4t-3=0\Leftrightarrow\left(2t+1\right)\left(2t-3\right)=0\)

\(t=\frac{3}{2}\)\(\Leftrightarrow\left(x^2+4x+4\right)=\frac{3}{2}\Leftrightarrow\int^{x=-2+\sqrt{\frac{3}{2}}}_{x=-2-\sqrt{\frac{3}{2}}}\)