Question

If (7x + 3)3 + (x - 2)3 + 27(2x - 5)3 = 9(7x + 3) × (x - 2) × (2x - 5) then the value of 5x + 3 is:
1. 2
2. 10
3. 6
4. 8

Answer 1

Correct Answer - Option 4 : 8

Given:

(7x + 3)3 + (x - 2)3 + 27(2x - 5)3 = 9(7x + 3) × (x - 2) × (2x - 5)

Formula:

When,

⇒ a + b = -c

then,

⇒ a³ + b³ + c³ = 3abc or vice versa

Calculation:

⇒ (7x + 3)³ + (x - 2)³ + 3(2x - 5)³ = 3 × (7x + 3) × (x - 2) × 3(2x - 5)

Then,

⇒ (7x + 3) + (x - 2) + 3(2x - 5) = 0

⇒ 7x + 3 + x - 2 + 6x - 15 = 0

⇒ 14x - 14 = 0

⇒ x = 1

Then,

⇒ 5x + 3 = 5 × 1 + 3 = 8

∴ 5x + 3 = 8