If $(4x - 5)^3 + (x - 2)^3 + 27(2x - 5)^3 = 9(4x -5)(x-2)(2x-5)$, then the value of $(x+\frac{3}{2})$ will be :
Answer & explanation
Correct answer: option 3
Given,
(4x - 5)3 + (x - 2)3+ 27(2x - 5)3= 9(4x - 5) (x - 2) (2x - 5)
We know,
If x + y + z = 0 then,
x3 + y3 + z3 = 3xyz
(4x - 5)3 + (x - 2)3+ 27(2x - 5)3= 9(4x - 5) (x - 2) (2x - 5)
= (4x - 5)3 + (x - 2)3+ 27(2x - 5)3 - 3(4x - 5) (x - 2) 3(2x - 5) = 0
= (4x - 5) + (x - 2) + 3(2x - 5) = 0
= 4x - 5 + x - 2 + 6x - 15 = 0
= 11x = 22
= x = 2
Put the value of x in the required equation,
$(x+\frac{3}{2})$ = $(2+\frac{3}{2})$ = $\frac{7}{2}$