If (4a+5 over a+5)=14 , what is the value of (16a²+25 over a²) ?

If (4a+5 over a+5)=14 , what is the value of (16a²+25 over…

If $(4a+{{5} \over a}+5)=14$ , what is the value of $(16a^2+{{25} \over a^2})$ ?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 41.

Formula used:

(a + b)² = a²+ b² + 2ab ---- (1)

Calculations:

⇒ 4a + 5/a = 14 - 5

Using equation (1), we get

⇒ 16a² + 25/a² + 2 × 4 × 5 = 81

⇒ 16a² + 25/a² = 81 - 40

⇒ 16a² + 25/a² = 41