Question

Tìm GTNN của

a, \(A=x^2+6x+10\)

b, \(B=x^2+6xy+9y^2+7\)

c, \(C=x^2+y^2-x+6y+10\)

Answer 1

a,

\(A=x^2+6x+10\)

=> \(A=\left(x+3\right)^2+1\ge1\forall x\)

Dấu "=" xảy ra ⇔ x = - 3

Vậy.....

b, \(B=x^2+6xy+9y^2+7\)

⇒ \(A=\left(x+3y\right)^2+7\ge7\forall x\)

Dấu "=" xảy ra ⇔ \(x=-3y\)

Vậy.....

c, \(C=x^2+y^2-x+6y+10\)

=> \(C=\left(x^2-x+\frac{1}{4}\right)+\left(y^2+6y+9\right)+\frac{3}{4}\)

=> \(C=\left(x-\frac{1}{2}\right)^2+\left(y+3\right)^2+\frac{3}{4}\ge\frac{3}{4}\forall x\)

Dấu "=" xảy ra ⇔ \(\left\{{}\begin{matrix}x=\frac{1}{2}\\y=-3\end{matrix}\right.\)

Vậy.......