Question

If a − 2b + 3c = 0; state the value of a³ − 8b³ + 27c³.

Answer 1

a − 2b + 3c = 0

a³ − 8b³ + 27c³

x³ + y³ + z³ − 3xyz = (x + y + z) (x² + y² + z² − xy − yz − zx)

a³ − (2b)³ + (3c)³ = a³ − 8b³ + 27c³

a³ + (−2b)³ + (3c)³

x + y + z = 0 ⇒ x³ + y³ + z³ = 3xyz

• x = a

• y = −2b

• z = 3c

a − 2b + 3c = 0 ⇒ x + y + z = 0

x³ + y³ + z³ = 3xyz ⇒ a³ + (−2b)³ + (3c)³ = 3(a) (−2b) (3c)

= 3⋅a⋅(−2b)⋅3c = −18abc

a³ − 8b³ + 27c³ = −18abc