If $(x+6)^3+(2 x+3)^3+(3 x+5)^3=(3 x+18)(2 x+3)(3 x+5)$, then what is the value of $x$ ?
Answer & explanation
Correct answer: option 3
(x + 6)3 + (2x + 3)3 + (3x + 5)3 = (3x + 18)(2x + 3)(3x + 5)
= (x + 6)3 + (2x + 3)3 + (3x + 5)3 = 3(x + 6) (2x + 3) (3x + 5)
Now,
If (a + b + c) = 0 then,
a3 + b3 + c3 = 3abc
= (x + 6) + (2x + 3) + (3x + 5) = 0
= 6x + 14 = 0
= 6x = -14
x = $-\frac{7}{3}$