Question
Download Solution PDFIf \(\frac{{{{\rm{x}}^2} + 1}}{{\rm{x}}} = 4\frac{1}{4}\), then what is the value of \({{\rm{x}}^3} + \frac{1}{{{{\rm{x}}^3}}}?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given that,
\(\frac{{{{\rm{x}}^2} + 1}}{{\rm{x}}} = 4\frac{1}{4}\)
⇒ x + 1/x = 17/4 ----(1)
Cubing both sides
(x + 1/x)3 = (17/4)3
We know that,
(a + b)3 = a3 + b3 + 3ab(a + b)
From equation (1),
⇒ x3 + 1/x3 + 3x(1/x)(x + 1/x) = (17/4)3
⇒ x3 + 1/x3 + 3x + 3/x = (17/4)3
⇒ (x3 + 1/x3) + 3(x + 1/x) = 4913/64
⇒ (x3 + 1/x3) = 4913/64 - 3 × (17/4)
⇒ (x3 + 1/x3) = 4097/64
Last updated on Jun 17, 2025
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