The min. Value

This question is given in arihant...

Prove that the min value of the expression x²+3y²+2xy-6x-3y is -11

Any hints on how to solve this ?

1 Answers

this was given just last week on the forum

see the question carefully there is a small mistake.. i am correcting that too...

x²+3y²+2xy-6x-2y

= (x+y)²+2y²-6x-2y

= (x+y)²+2y²-6(x+y)+4y

= (x+y-3)²-9+2(y²+2y+1)-2

=(x+y-3)²+2(y+1)² -11

the minima is achieved at y=-1, x=4

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