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10 February, 04:55

If (x + 1/x) ^2 = 3 what is the value of x^3 + 1/x^3

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  1. 10 February, 05:24
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    (x + 1/x) ² = 3 | √

    x + 1/x = √3

    According to short multiplication formula:

    (a + b) ³ = a³ + 3a²b + 3ab² + b³

    x³ + 1/x³ = (x) ³ + (1/x) ³ = (x + 1/x) ³ - 3x²/x - 3x/x² =

    = (x + 1/x) ³ - 3x - 3/x = (x + 1/x) ³ - 3 (x + 1/x) =

    = (√3) ³ - 3√3 = 3√3 - 3√3 = 0

    If (x + 1/x) ² = 3 the value of x³ + 1/x³ is 0.
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