Question

If a - 2b + 3c = 0; state the value of
a3 – 8b3 +27c3​

Answer 1

Answer:

Step-by-step explanation:

Hi ,

a + 2b + 3c = 0 ---( 1 )

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

( a + 2b )³ = ( - 3c )³

a³ + ( 2b )³ + 3 × a × 2b ( a + 2b ) = - 27c³

a³ + 8b³ + 27c³ + 6ab × ( - 3c ) = 0

[from ( 2 ) ]

a³ + 8b³ + 27c³ - 18abc = 0

a³ + 8b³ + 27c³ = 18abc

Hence proved .

I hope this helps you.

Answer 2

Answer:

Given:

a + 2b + 3c = 0, a + 2b = – 3c

Let us cube on both the sides, we get

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

a

3 + (2b)3 + 3(a) (2b) (a + 2b) = -27c3

a

3 + 8b3 + 6ab (– 3c) = – 27c3

a

3 + 8b3 – 18abc = -27c3

a

3 + 8b3 + 27c3 = 18abc

Hence proved.