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Step-by-step explanation:
x+1x=3x+1x=3
Taking cubes on both sides,
(x+1x)3=33(x+1x)3=33
Since,
(a+b)3=a3+3a2b+3ab2+b3(a+b)3=a3+3a2b+3ab2+b3
Therefore,
x3+3x2x+3xx2+1x3=27x3+3x2x+3xx2+1x3=27
x3+3x+3x+1x3=27x3+3x+3x+1x3=27
x3+1x3+3(x+1x)=27x3+1x3+3(x+1x)=27
x3+1x3+3(3)=27x3+1x3+3(3)=27
x3+1x3+9=27x3+1x3+9=27
x3+1x3=27−9x3+1x3=27−9
x3+1x3=18
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