Question

cách tìm gtnn của p= căn (x^2 -2xa+a^2) + căn (x^2 -2xb+b^2)

Answer 1

\(p=\sqrt{x^2-2xa+a^2}+\sqrt{x^2-2xb+b^2}\)

\(=\sqrt{\left(x-a\right)^2}+\sqrt{\left(x-b\right)^2}\)

\(=\left|x-a\right|+\left|x-b\right|\)

\(=\left|x-a\right|+\left|b-x\right|\ge\left|x-a+b-x\right|=\left|b-a\right|\)

Dấu \(=\)khi \(\left(x-a\right)\left(b-x\right)\ge0\).