Question

If 8a-64b-c = 24 cube root of abc is not equal to zero, then which of the following can be true? 1) 2 cube root of a - 4 cube root of b - cube root of c = 0 2) 2 cube root of a = 4 cube root of b = cube root of c. 3) a+b+c=0 4) a=b=c.

Answer 1

hey mate
here's the solution

Answer 2

<<HEY MATE HERE'S YOUR ANSWER>>
8a - 64b - c = 24* cube root abc ( GIVEN)

Here, LHS =

{2 (cube root a)}^3 - {4(cube root b)}^3 -(cuberoot c)^3

RHS =

3* 2(cube root a)  4*(cube root b) cube root c

If we assume 2(cube root a) =  -4(cube root b) =  & - (cube root c ) = 

Then,  x^3 + y^3 + z^3 &  

Using 

So, here, x + y + z = 0

=> 2 (cube root a) - 4(cube root b) - ( cube root c) = 0

=> 2 a^1/3 - 4b^1/3 - c^1/3 = 0

Since no other relations of a, b, c given. So, 

As, 2* 8^1/3 - 4*27^1/3 - (- 512)^1/3

= 4 - 12 + 8 = 0

So, LHS = 8a -64b-c = 8*8 - 64*27 - -512 = 64–1728 +512 = -1152

RHS = 24 * cube root abc = 24* cube root (8*27*-512) = 24 * -48 = -1152

HOPE IT HELPS
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