Question Details

If a+2b+3c=0, then what is the value of (a3+8b3+27c3)?

Options

A

18 abc

B

12 abc

C

6 abc

D

0

Show Answer

Correct Answer :

Option A

18 abc

Solution :

The correct answer is 18 abc.

Step-by-step explanation:

We use the standard algebraic identity:

If x+y+z=0, then:

x3+y3+z3=3xyz

Let us assign:

x=a

y=2b

z=3c

We are given that:

a+2b+3c=0

Since x+y+z=0, we can apply the identity directly:

(a)3+(2b)3+(3c)3=3(a)(2b)(3c)

Simplifying the terms:

(2b)3=8b3

(3c)3=27c3

3(a)(2b)(3c)=18abc

Substituting these simplified terms back into the equation:

a3+8b3+27c3=18abc

Thus, the value of (a3+8b3+27c3) is 18 abc.

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