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

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

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

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