Question

(x^2-7x+12).(x^2-3x+2)=8

Answer 1

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)=8\)

\(\Leftrightarrow\left(x^2-5x+4\right)\left(x^2-5x+6\right)=8\)

\(\Leftrightarrow\left(x^2-5x\right)^2+10\left(x^2-5x\right)+24-8=0\)

\(\Leftrightarrow\left(x^2-5x\right)^2+10\left(x^2-5x\right)+16=0\)

\(\Leftrightarrow\left(x^2-5x+2\right)\left(x^2-5x+8\right)=0\)

\(\Leftrightarrow x^2-5x+2=0\)

\(\text{Δ}=\left(-5\right)^2-4\cdot1\cdot2=25-8=17>0\)

Do đó: PT có 2 nghiệm phân biệt là;

\(\left\{{}\begin{matrix}x_1=\dfrac{5-\sqrt{17}}{2}\\x_2=\dfrac{5+\sqrt{17}}{2}\end{matrix}\right.\)