Question
If [x + (1/x) ] = 4, then find the value of [x 3Â + (1/x 3) ].
Solution
x + (1/x) = 4 On squaring both sides, We get, [x + (1/x) ]2Â = 42 Or, x2Â + (1/x2) + 2 = 16 Or, x2Â + (1/x2) = 14 ------- (I) Using a3Â + b3Â = (a + b) (a2Â + b2Â - ab) x3Â + (1/x3) = [x + (1/x) ][x2Â + (1/x2) - 1] = 4 X (14 - 1) (From equation I) = 4 X 13 = 52
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