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Question

The least value of expression x24xy+5y22y+6, if x,yR is

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Solution

f(x,y)=x24xy+5y22y+6
=x22x(2y)+(2y)2+y22y+1+5
=(x2y)2+(y1)2+5
5

Hence, least value of f(x,y) is 5.

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