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If x3+1/x3=110, then find the value …

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If x3+1/x3=110, then find the value of x+1/x

    • Posted by Yuvraj Kasana 6 years, 5 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Yogita Ingle 6 years, 5 months ago

    Given x3+ 1/x3 =110
    Recall that (x+1/x)3 = x3+ 1/x3 + 3(x+1/x)
    Let (x+1/x)=a
    ⇒ a3 = 110 + 3a
    ⇒a3 − 3a −110=0
    Put a=5
    ⇒ 53 − 3(5) −110
    =125 −15 −110=0
    Hence (a − 5) is a factor.
    On dividing (a3 − 3a −110) with (a − 5) we get the quotient as (a2+5a+22)
    ∴ a3 − 3a −110 = (a − 5)(a2+5a+22) = 0
    Hence (a − 5) = 0 and (a2+5a+22) ≠ 0
    ⇒(x+1/x) − 5=0
    ∴ (x+1/x) = 5

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