If \(5a + \frac{1}{{7a}} = 5\), then find the value of \(49{a^2} + \frac{1}{{25{a^2}}} = ?\)
If \(5a + \frac{1}{{7a}} = 5\), then find the value of \(49{a^2} + \frac{1}{{25{a^2}}} = ?\)
1). 284/8
2). 235/7
3). 231/5
4). 261/6
1 answers
$({\rm{E}} = 5a + \frac{1}{{7a}} = 5)$
Multiplying both the sides by 7/5,
$(\frac{7}{5} \times 5a + \frac{1}{{7a}} \times \frac{7}{5} = 5 \times \frac{7}{5})$
$(\Rightarrow 7a + \frac{1}{{5a}} = 7)$
Squaring both the sides, we get,
$(\begin{array}{l} \Rightarrow 49{a^2} + \frac{1}{{25{a^2}}} + 2 \times 7a \times \frac{1}{{5a}} = 49\\ \Rightarrow 49{a^2} + \frac{1}{{25{a^2}}} = 49 - \frac{{14}}{5}\\ \Rightarrow 49{a^2} + \frac{1}{{25{a^2}}} = \frac{{231}}{5} \end{array})$
∴ Answer is 231/5Other Questions
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