Bài 1: Tìm x
a) Ta có: \(4x\left(x+2\right)-7\left(2x-1\right)+9\left(3x-4\right)=30\)
\(\Leftrightarrow4x^2+8x-14x+7+27x-36-30=0\)
\(\Leftrightarrow4x^2+21x-59=0\)
\(\Leftrightarrow4\left(x^2+\frac{21}{4}x-\frac{59}{4}\right)=0\)
\(\Leftrightarrow x^2+\frac{21}{4}x-\frac{59}{4}=0\)
\(\Leftrightarrow x^2+2\cdot x\cdot\frac{21}{8}+\frac{441}{64}-\frac{1385}{64}=0\)
\(\Leftrightarrow\left(x+\frac{21}{8}\right)^2=\frac{1385}{64}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{21}{8}=\frac{\sqrt{1385}}{8}\\x+\frac{21}{8}=-\frac{\sqrt{1385}}{8}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{1385}-21}{8}\\x=\frac{-\sqrt{1385}-21}{8}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{\sqrt{1385}-21}{8};\frac{-\sqrt{1385}-21}{8}\right\}\)
Bài 2: Thực hiện phép tính
a) Ta có: \(\left(x+3\right)\left(x^2+3x-5\right)\)
\(=x^3+3x^2-5x+3x^2+9x-15\)
\(=x^3+6x^2+4x-15\)
b) Ta có: \(\left(x+1\right)\left(x^2-x+1\right)\)
\(=x^3+1\)
c) Ta có: \(\left(x^2-2x+3\right)\left(x-4\right)\)
\(=x^3-4x^2-2x^2+8x+3x-12\)
\(=x^3-6x^2+11x-12\)
