Question : If $(4a + \frac{5}{a} + 5)=14$, what is the value of $(16a^2+ \frac{25}{a^2})$?
Option 1: 25
Option 2: 36
Option 3: 41
Option 4: 40
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Answer (1)
24th Jan, 2024
Correct Answer: 41
Solution :
$(4a + \frac{5}{a} + 5) = 14$
$⇒(4a + \frac{5}{a}) = 14-5 = 9$
$⇒(4a + \frac{5}{a})^2 = 9^2$
$⇒(16a^2+ \frac{25}{a^2} + 40) = 81$
$\therefore(16a^2+ \frac{25}{a^2})= 81-40 = 41$
Hence, the correct answer is 41.
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