Correct Answer - Option 4 : 25
Given:
x(x - 5) = 7
⇒ x2 – 5x = 7
Concept:
Cube both side of the given equation and then proceed.
Formula used:
(a - b)3 = a3 - b3 - 3ab(a - b)
Calculation:
∵ x2 - 5x = 7
On cubing both sides, we get;
(x2 – 5x)3 = 73
⇒ x6 - 125x3 – [3 × (x2) × 5x(x2 – 5x)] = 343
⇒ x6 - 125x3 - [3 × x2 × (5x) × (7)] = 343
⇒ x6 - 125x3 - 105x3 = 343
⇒ x6 – 230x3 = 343 ------(1)
Putting the value of (1) in (x6 – 230x3 – 243)/4;
⇒ (343 – 243)/4
⇒ 100/4 = 25