Question

If u, v, w are real numbers such that u^3-8v^3-27w^3=8uw, which one of the following is correct?
(A) u-v+w=0
(B) u=-v=-w
(C) u-2v=3w
(D) u+2v=-3w

EXPLAIN YOUR ANSWER

Answer 1

The correct answer is (c) u-2v=3w

Given,

If u, v, w are real numbers such that u^3-8v^3-27w^3=18uvw

To find,

If u, v, w are real numbers such that u^3-8v^3-27w^3=18uvw, what will be the simple expression of u,v, and w

Solution,

The given expression is u^3-8v^3-27w^3=18uvw

where u, v, w are real numbers

The constants 8, and 27 are perfect cubes of 2 and 3 respectively,

so we can elaborate on the given expression in the form of cubes,

we get.,

=> (u)^3 + (– 2v)^3 + (– 3w)^3 = 3 × (– 2)( – 3) uvw

=> u + (– 2v) + (– 3w) = 0

=> u – 2v – 3w = 0

=> u – 2v = 3w

Therefore, the correct answer is (c) u-2v=3w

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