Question

Giải PT:

     ( x² - 5x )² + 10 ( x² - 5x ) + 24 = 0

Answer 1

\(\left(x^2-5x\right)^2+10\left(x^2-5x\right)+24\)

Đặt \(a=x^2-5x\Rightarrow a^2=\left(x^2-5x\right)^2\)

Thay vào đẳng thức ta có:

\(a^2+10a+24\)

\(=a^2+6a+4a+24\)

\(=a\left(a+6\right)+4\left(a+6\right)\)

\(=\left(a+4\right)\left(a+6\right)\)

\(=\left(x^2-5x+6\right)\left(x^2-5x+4\right)\)

\(=\left(x^2-2x-3x+6\right)\left(x^2-x-4x+4\right)\)

\(=\left[x\left(x-3\right)-2\left(x-3\right)\right]\left[\left(x-1\right).x-4\left(x-1\right)\right]\)

\(=\left(x-3\right)\left(x-2\right)\left(x-4\right)\left(x-1\right)\)