Question

Tìm GTNN : A = \(5x^2-x-2\)

Answer 1

A = \(5\left(x^2-\frac{1}{5}x-\frac{2}{5}\right)=5\left(x^2-2.x\cdot\frac{1}{10}+\frac{1}{100}-\frac{1}{100}-\frac{2}{5}\right)\)

   = \(5\left(\left(x-\frac{1}{10}\right)^2-\frac{41}{100}\right)=5\left(x-\frac{1}{10}\right)^2-\frac{41}{100}.5=5\left(x-\frac{1}{10}\right)^2-\frac{41}{20}\)

Vì 5 (x-1/10)^2 \(\ge\)  0 => \(5\left(x-\frac{1}{10}\right)^2-\frac{41}{20}\ge-\frac{41}{20}\)

Vậy MiNa = -41/20 khi x-1/10 = 0 => x = 1/10