If (3(16³ - 6³))/((16² + 6² + Q)) =30, then find the value of Q.

If (3(16³ - 6³))/((16² + 6² + Q)) =30, then find the value…

If $\frac {3(16^3 - 6^3)} {(16^2 + 6^2 + Q)} =30,$ then find the value of Q.

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 96.

a³ - b³ = (a - b)(a² + ab + b²)

Now, $\frac {3(16^3 - 6^3)} {(16^2 + 6^2 + Q)} =30$

⇒ $\frac {(16^3 - 6^3)} {(16^2 + 6^2 + Q)} =10$

⇒ 16³ - 6³ = 10(16² + 6² + Q)

⇒ (16 - 6)(16² + 96 + 6²) = 10(16² + 6² + Q)

⇒ 10(16² +96 + 6²) = 10(16² + 6² + Q)

⇒ 16² + 96 + 6² = 16² + 6² + Q

⇒ Q = 96

Therefore, the value of Q is 96.