e) x³ - 7x + 6 = 0
x³ - x² + x² - x - 6x + 6 = 0
(x³ - x²) + (x² - x) - (6x - 6) = 0
x²(x - 1) + x(x - 1) - 6(x - 1) = 0
(x - 1)(x² + x - 6) = 0
(x - 1)(x² - 2x + 3x - 6) = 0
(x - 1)[(x² - 2x) + (3x - 6)] = 0
(x - 1)[x(x - 2) + 3(x - 2)] = 0
(x - 1)(x - 2)(x + 3) = 0
x - 1 = 0 hoặc x - 2 = 0 hoặc x + 3 = 0
*) x - 1 = 0
x = 1
*) x - 2 = 0
x = 2
*) x + 3 = 0
x = -3
Vậy x = -3; x = 1; x = 2
g: \(\left(x+2\right)\left(x+3\right)\left(x-7\right)\left(x-8\right)=144\)
=>\(\left(x+2\right)\left(x-7\right)\left(x+3\right)\left(x-8\right)=144\)
=>\(\left(x^2-5x-14\right)\left(x^2-5x-24\right)=144\)
=>\(\left(x^2-5x\right)^2-24\left(x^2-5x\right)-14\left(x^2-5x\right)+336-144=0\)
=>\(\left(x^2-5x\right)^2-38\left(x^2-5x\right)+192=0\)
=>\(\left(x^2-5x\right)^2-6\left(x^2-5x\right)-32\left(x^2-5x\right)+192=0\)
=>\(\left(x^2-5x\right)\left(x^2-5x-6\right)-32\left(x^2-5x-6\right)=0\)
=>\(\left(x^2-5x-6\right)\left(x^2-5x-32\right)=0\)
=>\(\left(x-6\right)\left(x+1\right)\left(x^2-5x-32\right)=0\)
=>\(\left[{}\begin{matrix}x-6=0\\x+1=0\\x^2-5x-32=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-1\\x=\dfrac{5\pm3\sqrt{17}}{2}\end{matrix}\right.\)
g: \(\left(x^2-11x+28\right)\left(x^2-7x+10\right)=72\)
=>\(\left(x-4\right)\cdot\left(x-7\right)\cdot\left(x-2\right)\cdot\left(x-5\right)=72\)
=>\(\left(x-4\right)\left(x-5\right)\left(x-7\right)\left(x-2\right)=72\)
=>\(\left(x^2-9x+20\right)\left(x^2-9x+14\right)=72\)
=>\(\left(x^2-9x\right)^2+14\left(x^2-9x\right)+20\left(x^2-9x\right)+280-72=0\)
=>\(\left(x^2-9x\right)^2+34\left(x^2-9x\right)+208=0\)
=>\(\left(x^2-9x\right)^2+26\left(x^2-9x\right)+8\left(x^2-9x\right)+208=0\)
=>\(\left(x^2-9x\right)\left(x^2-9x+26\right)+8\left(x^2-9x+26\right)=0\)
=>\(\left(x^2-9x+8\right)\left(x^2-9x+26\right)=0\)
=>\(\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)=0\)
mà \(x^2-9x+26=x^2-2\cdot x\cdot4,5+20,25+5,75=\left(x-4,5\right)^2+5,75>0\forall x\)
nên (x-1)(x-8)=0
=>\(\left[{}\begin{matrix}x-1=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=8\end{matrix}\right.\)
