Question

(x²-x+1)(x²-x+2)=12

Giải dùm với ạ :))

Answer 1

(x² - x + 1)(x² - x + 2) = 12           (*)

Đặt \(x^2-x+\frac{3}{2}=t\) \(=\left(x-\frac{1}{2}\right)^2+\frac{5}{4}\)

(*) trở thành \(\left(x-\frac{1}{2}\right)\left(t+\frac{1}{2}\right)-12=0\)

\(\Leftrightarrow t^2-\frac{1}{4}-12=0\)

\(\Leftrightarrow t^2=12+\frac{1}{4}=\frac{49}{4}\)

=> \(\left[\left(x-\frac{1}{2}\right)^2+\frac{5}{4}\right]^2=\frac{49}{4}\)

Lại có:\(\left(x-\frac{1}{2}\right)^2+\frac{5}{4}\ge\frac{5}{4}\forall x\)

nên \(\left(x-\frac{1}{2}\right)^2+\frac{5}{4}=\frac{7}{2}\)

đến đây dễ r`