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Question

If x2+y2=10,xy=5, find the value of x4+y4.

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Solution

x2+y2=10 and xy=5x2+y22=102x4+y4+2x2y2=100x4+y4+2xy2=100x4+y4+252=100x4+y4+50=100x4+y4=50

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