Question

tìm min

A=(x-5)²+(x+1)²+5

giải gúp mình mình đang cần gấp

Answer 1

\(A=\left(x-5\right)^2+\left(x+1\right)^2+5=x^2-10x+25+x^2+2x+1+5.\)

\(=2x^2-8x+31=2\left(x^2-4x\right)+31=2\left(x^2-2.x.2+4\right)-8+31\)

\(=2\left(x-2\right)^2+23\)

Vì \(2\left(x-2\right)^2\ge0\forall x\)nên \(2\left(x-2\right)^2+23\ge23\forall x\)

Vậy \(MinA=23\Leftrightarrow2\left(x-2\right)^2=0\Leftrightarrow x=2\)