Question

Tìm GTNN của

a) Q=x\(^2\)+10x+30

b) Q= x\(^2\)-x+1

Answer 1

a: \(Q=x^2+10x+25+5=\left(x+5\right)^2+5>=5\)

Dấu '=' xảy ra khi x=-5

b: \(Q=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>=\dfrac{3}{4}\)

Dấu '=' xảy ra khi x=1/2

Answer 2

a)Ta có \(Q=x^2+10x+30=x^2+10x+25+5=\left(x+5\right)^2+5\ge5\)

Dấu = xảy ra <=> x = -5

b)Ta có\(Q=x^2-x+1=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)

Dấu = xảy ra <=> x = 1/2