Question

Tìm GTNN

\(\left(x+1\right)^2+\left(x+2\right)^2+\left(x+3\right)^2+\left(x+4\right)^2\)

Answer 1

\(a=\left(x+1\right)^2+\left(x+2\right)^2+\left(x+3\right)^2+\left(x+4\right)^2\)

\(a=\left(x^2+2x+1\right)+\left(x^2+4x+4\right)+\left(x^2+6x+9\right)+\left(x^2+8x+16\right)\)

\(a=x^2+2x+1+x^2+4x+4+x^2+6x+9+x^2+8x+16\)

\(a=\left(x^2+x^2+x^2+x^2\right)+\left(2x+4x+6x+8x\right)+\left(1+4+9+16\right)\)

\(a=4x^2+20x+30\)

\(a=4x^2+20x+25+5\)

\(a=\left(2x+5\right)^2+5\ge5\)

Dấu "=" xảy ra khi: \(x=-\dfrac{5}{2}\)