Question

it is given that 3a+2b=5c ,then find the value of 27a^3 +8b^3 -125c^3 if abc= 0

Answer 1

Hi ,

3a + 2b = 5c ------( 1 )

abc = 0 -------( 2 )

27a³ + 8b³ - 125c³

= ( 3a )³ + ( 2b )³ + ( -5c )³

=(3a+2b-5c)[(3a)²+(2b)²+(-5c)²-3a×2b-(2b)(-5c)-

(-5c)(3a)] + 3(3a )(2b )( -5c)

= 0 - 90abc { since equation ( 1 ) }

= - 90abc

= ( - 90 ) × 0 { from ( 2 ) }

= 0

I hope this helps you.

:)

Answer 2

(3a + 2b -5c) = 0
(3a + 2b -5c)³ = 0
Using the formula, (a + b + c)³ = a³ + b³ + c³+3a²b+3a²c + 3b²c +3b²a +3c²a +3c²a+6abc 
we get
(3a + 2b -5c)³ = 27a³ + 8b³ - 125c³ + 27a²b +27a²c + 12b²c + 12b²a + 75c²a +75c²b - 180abc = 0

∵abc = 0
⇒27a³ + 8b³ - 125c³ =0

hope it helped.
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