If (5a + 4/a - 2)=13 and a > 0, what is the value of (25²+16/(a²)) ?

If (5a + 4/a - 2)=13 and a > 0, what is the value of…

If (5a + $\frac{4}{a}$ - 2)=13 and a > 0, what is the value of $(25^2+\frac{16}{a^2})$ ?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 185.

5a + (4/a) - 2 = 13

⇒ 5a + (4/a) = 13 + 2 = 15

⇒ [5a + (4/a)]² = 15²

⇒ (5a)² + 2(5a)(4/a) + (4/a)² = 225

⇒ 25a² + 40 + 16/a² = 225

⇒ 25a² + 16/a² = 225 - 40 = 185

Therefore, the value of the expression is 185.