Question

Tìm min:

(x+1)(x+2)(x+8)(x+9)

Answer 1

\(a=\left(x+1\right)\left(x+2\right)\left(x+8\right)\left(x+9\right)\)

\(a=\left[\left(x+1\right)\left(x+9\right)\right]\left[\left(x+2\right)\left(x+8\right)\right]\)

\(a=\left[x\left(x+9\right)+1\left(x+9\right)\right]\left[x\left(x+8\right)+2\left(x+8\right)\right]\)

\(a=\left(x^2+9x+x+9\right)\left(x^2+8x+2x+16\right)\)

\(a=\left(x^2+10x+9\right)\left(x^2+10x+16\right)\)

\(a=\left(x^2+10x+12,5-3,5\right)\left(x^2+10x+12,5+3,5\right)\)

\(a=\left(x^2+10x+12,5\right)^2-\dfrac{49}{4}\ge-\dfrac{49}{4}\)