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Question

If xy+yx=1 (x,y0), find the value of x3y3

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Solution

xy+yx=1

x2+y2xy=1

x2+y2=1xy

x2+y2+xy=0(i)

Using the identity, x3y3=(xy)(x2+xy+y2)(ii)

on putting the value of equation (i) in equation (ii), we get

x3y3=0


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