Question
Download Solution PDFIf \(\left( {4a + \frac{5}{a} + 5} \right)\) = 14, what is the value of \(\left( {16{a^2} + \frac{{25}}{{{a^2}}}} \right)\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\left( {4a + \frac{5}{a} + 5} \right)\) = 14
Concept used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
\(\left( {4a + \frac{5}{a} + 5} \right)\) = 14
⇒ \({4a + \frac{5}{a}}\) = 9
⇒ \(({4a + \frac{5}{a}})^2\) = 92
⇒ \({16{a^2} + \frac{{25}}{{{a^2}}}+2.4a.\frac{5}{a}}\) = 81
⇒ \({16{a^2} + \frac{{25}}{{{a^2}}}+40}\) = 81
⇒ \({16{a^2} + \frac{{25}}{{{a^2}}}}\) = 41
∴ The required answer is 41.
Last updated on Jul 12, 2025
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