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The least value of the expression x^2 + 2y^2 + 2xy +4y +7 is

The least value of the expression x^2 + 2y^2 + 2xy +4y +7 is

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

f(x,y) = x^{2}+2y^{2}+2xy+4y+7
f(x,y) = x^{2}+y^{2}+2xy+y^{2}+4y+7
f(x,y) = x^{2}+y^{2}+2xy+y^{2}+4y+4 + 3
f(x,y) = (x+y)^{2}+(y+2)^{2}+ 3
x, y belong to R.
Minimum will of the square of any real number is zero.
Minima of f(x, y) will be at
x = 2, y = -2
[f(x,y)]_{min} = (2+(-2))^{2}+(-2+2)^{2}+ 3
[f(x,y)]_{min} = 3

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