Question

Tìm GTNN của biểu thức

H= |x-3|+|4-x|

A=x(x+2)+2(x-\(\frac{3}{2}\))

Answer 1

\(H=|x-3|+|4-x|\ge|x-3+4-x|=1\)

Dấu "=" xảy ra <=> x=3

Answer 2

\(H=\left|x-3\right|+\left|4-x\right|\ge\left|x-3+4-x\right|=1\)

Dau "=" xra  <=>  \(\left(x-3\right)\left(4-x\right)\ge0\)  ,=>  \(3\le x\le4\)

Answer 3

\(A=x\left(x+2\right)+2\left(x-\frac{3}{2}\right)\)

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

\(=x^2+4x-3\)

\(=x^2+4x+4-7=\left(x+2\right)^2-7\ge-7\)

Dau "=" xra  <=> x = -7

Vay...