Question

tim gia tri nho nhat cua cac da thuc

Q=2 x mũ 2 - 6x

M = x mũ 2 +y mũ 2-x+6y+10

Answer 1

\(Q=2x^2-6x\)

\(Q=2.(x^2 - 2.\dfrac{3}{2}.x+\dfrac{9}{4}\text{)}-\dfrac{9}{2} \)

\(Q=2.(x-\dfrac{3}{2})^2-\dfrac{9}{2}\ge\dfrac{-9}{2}\)

\(\Rightarrow Min_A=\dfrac{-9}{2}\) khi \(x=\dfrac{3}{2}\) .

\(M=x^2+y^2-x+6y+10\)

\(M=\left(x^2-x+\dfrac{1}{4}\right)+\left(y^2+6y+9\right)+\dfrac{3}{4}\)

\(M=\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2+\dfrac{3}{4}\)

\(M=\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2\ge0\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)

\(\Rightarrow Min_M=\dfrac{3}{4}\) khi \(x=\dfrac{1}{2},y=-3.\)