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Question

For all real value of x and y , x2+2xy+3y26y92

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Solution

Given, x2+2xy+3y26y

=(x+y)2+2y26y

=(x+y)2+2y(y3)

thus it attains its min value when 2y(y-3) attains its min value
at y=3/2 it attains min value with 92

at x=y(x+y)2 is minimum
thus x2+2xy+3y26y92

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