31x^4+x^4 + 2x^2(1/x^2) = 322+2
(x^2+(1/x^2))^2 = 324
x^2+(1/x^2)= 18
x^2+(1/x^2)- 2x(1/x) = 18-2
x-(1/x)=4
Now cubing both sides
x^3 - (1/x^3) - 3x(1/x)(x-(1/x)) = 64
x^3-(1/x^3) - 3.4 =64
x^3-(1/x^3) = 64 + 12 = 76
And there you have it as b
3 Answers
3169x4 + 1x4 = 322
or, (x2)2 + (1x2)2 + 2.x2.1x2
= 322 + 2 = 324 = 182
or, (x2 + 1x2)2 = 182
or, x2 + 1x2 = 18
or, x2 + (1x)2 - 2.x.1x
= 18-2 = 16 = 42
69Continuing with the sum,
(x - 1x)2 = 42
or, x - 1x = 4
or, (x - 1x)3 = 43
or, x3 - 3.x2.1x + 3.x.(1x)2 - 1x3 = 64
Therefore, x3 - 1x3 - 3x + 3x = 64
Therefore, x3 - 1x3 -3(x - 1x) = 64
Therefore,
x3 - 1x3 - 3 * 4 = 64
Or, x3 - 1x3 - 12 = 64
Or, x3 - 1x3 = 64 + 12 = 76
Ans) x3 - 1x3 = 64 + 12 = 76
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