SSC CGL Tier-2 12th September 2019 Maths

Question 53

If $$(5x + 1)^3 + (x - 3)^3 + 8(3x - 4)^3 = 6(5x + 1)(x - 3)(3x - 4)$$,$$ then $$x$$ is equal to:

Solution

$$(5x + 1)^3 + (x - 3)^3 + 8(3x - 4)^3 = 6(5x + 1)(x - 3)(3x - 4)$$
$$(5x + 1)^3 + (x - 3)^3 + (6x - 8)^3= 3(5x + 1)(x - 3)(6x - 8)$$
When $$a^3 + b^3 + c^3$$ = 3abc then a + b + c = 0.
5x + 1 + x - 3 + 6x - 8 = 0
12x = 10
x = 5/6


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