Question
If x2Â = 15x + 1, then find the value of
{x3Â - (1/x3) }.Solution
We have, x2Â = 15x + 1Divide both sides by 'x', x = 15 + (1/x) so, (x - 1/x) = 15 Cubing both sides, (x - 1/x)3 = 153 Using, (a - b)Â 3Â = a3Â - b3Â - 3ab(a - b) (x - 1/x)3 =Â x3Â - (1/x)3Â - 3(x - 1/x) 153 = x3Â - (1/x)3Â - 3 x 15 So, (x - 1/x)3Â = 2275 + 45 = 3420
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