Question

tìm GTNN:

A=\(x^2+11y^2+6xy-2y+5\)

\(C=2x^2+x-5\)

\(B=2x^2+2xy+2y^2-4x-4y+15\)

Answer 1

2C=4x^2+2x-10=((2x)^2+4x\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\))-\(\dfrac{41}{4}\)

=\(\left(2x+\dfrac{1}{2}\right)^2\)-41/4\(\ge\dfrac{-41}{4}\)

=> C\(\ge\dfrac{-41}{8}\)

Vậy min C = \(\dfrac{-41}{8}\)khi x=\(\dfrac{-1}{4}\)

Answer 2

\(4A=4x^2+44y^2+24xy-8y+20=\left(2x\right)^2+2.2x.6y+\left(6y\right)^2+8y^2-8y+20=\left(2x+6y\right)^2+2\left(4y^2-4y+1\right)+18=\left(2x+6y\right)^2+2\left(2y-1\right)^2+18\ge18\)

Answer 3

min A =18/4=4.5 khi x=-1.5,y=0.5