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Question

If x^2+y^2=29,and xy=2,find the value of x+y,x-y and x^4+y^4.


Solution

x2+y2=29,xy=2(i)(x+y)2=x2+y2+2xy=29+2×2=29+4=33x+y=±33(ii)(xy)2=x2+y22xy=292×2=294=25xy=±25=±5(iii)x2+y2=29
Squaring on both sides,(x2+y2)2=(29)2(x2)2+(y2)2+2x2y2=841x4+y4+2(xy)2=841x4+y4+2(2)2=841(xy=2)x4+y4+2×4=841x4+y4+8=841x4+y4=8418=833x4+y4=833

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