Question

Tìm GTLN của biểu thức:

a) \(-3x^2-6x+4\)

b) \(-x^2+3x-1\)

c) \(\left(x+1\right)^2+\left(2x-1\right)^2-6x^2\)

d) \(-\left(2x^2+4y^2+4xy-2x-3\right)\)

Answer 1

\(A=-3\left(x+1\right)^2+7\le7\)

\(A_{max}=7\) khi \(x=-1\)

\(B=-\left(x-\frac{3}{2}\right)^2+\frac{5}{4}\le\frac{5}{4}\)

\(B_{max}=\frac{5}{4}\) khi \(x=\frac{3}{2}\)

\(C=-x^2-2x+2=-\left(x+1\right)^2+3\le3\)

\(C_{max}=3\) khi \(x=-1\)

\(D=-\left[\left(x+2y\right)^2+\left(x-1\right)^2-4\right]=-\left(x+2y\right)^2-\left(x-1\right)^2+4\le4\)

\(D_{max}=4\) khi \(\left\{{}\begin{matrix}x=1\\y=-\frac{1}{2}\end{matrix}\right.\)