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 :

8

We know that,

When,

a + b + c = 0 then,

= a³ + b³ + c³ = 3abc or vice versa

= (7x + 3)³ + (x - 2)³ + 3³(2x - 5)³ = 3 × (7x + 3) × (x - 2) × 3(2x - 5)

a = 7x + 3, b = x - 2 and c = 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