Question

Tìm min, max: a) A= (2x - 3)(1 + 3x)

                        b) B= (3 - 2x)(1 + 4x)

Answer 1

a; \(A=2x+6x^2-3-9x\)

\(=6x^2-7x-3\)

\(=6\left(x^2-\dfrac{7}{6}x-\dfrac{1}{2}\right)\)

\(=6\cdot\left(x^2-2\cdot x\cdot\dfrac{7}{3}+\dfrac{49}{6}-\dfrac{26}{3}\right)\)

\(=6\left(x-\dfrac{7}{3}\right)^2-52\ge-52\forall x\)

Dấu '=' xảy ra khi x=7/3

b: \(B=3+12x-2x-8x^2\)

\(=-8x^2+10x+3\)

\(=-8\left(x^2-\dfrac{5}{4}x-\dfrac{3}{8}\right)\)

\(=-8\left(x^2-2\cdot x\cdot\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{53}{8}\right)\)

\(=-8\left(x-\dfrac{5}{2}\right)^2+53\le53\forall x\)

Dấu '=' xảy ra khi x=5/2