Question

If x+1x=7, find x3+1x3.

Solution
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It is given that x+1x=7, by taking cubes on both sides we get:

(x+1x)3=73(x)3+(1x)3+(3×x×1x)(x+1x)=343((a+b)3=a3+b3+3ab(a+b))x3+1x3+3(7)=343(Givenx+1x=7)x3+1x3+(3×7)=343
x3+1x3+21=343x3+1x3=34321x3+1x3=322

Hence, x3+1x3=322.

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