Question

Tim GTNN cua : D = x^2 - x + 1

E = x.(x-3)

G = x^2 + 5y^2 + 2xy - 2y + 100

Mn giup e vs <3

Answer 1

\(D=x^2-x+1=\left(x^2-x+\frac{1}{4}\right)+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)

Vậy GTNN của D là \(\frac{3}{4}\)khi x = \(\frac{1}{2}\)

\(E=x\left(x-3\right)=x^2-3x=\left(x^2-3x+\frac{9}{4}\right)-\frac{9}{4}=\left(x-\frac{3}{2}\right)^2-\frac{9}{4}\ge-\frac{9}{4}\)

Vậy GTNN của E là \(-\frac{9}{4}\)khi x = \(\frac{3}{2}\)

\(G=x^2+5y^2+2xy-2y+100\)

\(G=\left(x^2+2xy+y^2\right)+\left(4y^2-2y+\frac{1}{4}\right)+\frac{399}{4}\)

\(G=\left(x+y\right)^2+\left(2y-\frac{1}{2}\right)^2+\frac{399}{4}\ge\frac{399}{4}\)

Vậy GTNN của G là \(\frac{399}{4}\)khi x = \(-\frac{1}{4}\); y = \(\frac{1}{4}\)

Answer 2

Hihiii cam on bann nhieuu nhe <3