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When x(x - 5) = 7, then find the value of (x6 – 230x3 – 243)/4?

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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

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