Question
Download Solution PDFIf, for a non-zero x, 5x2 + 7x + 5 = 0, then the value of \({x^3} + \frac{1}{{{x^3}}}\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
5x2 + 7x + 5 = 0
Calculations:
According to question,
5x2 + 7x + 5 = 0
⇒5x² + 5 = - 7x
⇒5x(x + 1/x) = - 7x
⇒x + 1/x = -7/5
so, x³ + 1/x³
= (-7/5)³ - 3 × (-7/5)
= - 343/125 + 21/5
= (-343 + 525 )/125
= 182/125
Hence, The Required value is 182/125.
Last updated on Jul 21, 2025
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