If (2x + 3)3 + (x - 8)3 + (x 13)3 = (2x + 3)(3x - 24)(x + 13), then what is the value of x?
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. -2
(2x + 3)3 + (x - 8)3 + (x + 13)3 = (2x + 3)(3x - 24)(x + 13) = 3(2x + 3)(x - 8)(x + 13)
Let,
a = 2x + 3, b = x - 8, c = x + 13
Since, a3 + b3 + c3 = 3abc
So, a + b + c = 0
⇒ 2x + 3 + x - 8 + x + 13 = 0
⇒ 4x = -8
⇒ x = -2