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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
7 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
Minimum value of square of any number is zero. Minima 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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