If a?+b?+c?=0, then (a+b+c)3= 27abc. how

Asked by manavmansvi | 31st Aug, 2014, 07:44: PM

Expert Answer:

G i v e n space t h a t space a to the power of 1 third end exponent plus b to the power of 1 third end exponent plus c to the power of 1 third end exponent equals 0 T h a t space i s space a to the power of 1 third end exponent plus b to the power of 1 third end exponent equals minus c to the power of 1 third end exponent N o w space c u b i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma open parentheses a to the power of 1 third end exponent plus b to the power of 1 third end exponent close parentheses cubed equals open parentheses minus c to the power of 1 third end exponent close parentheses cubed... left parenthesis 1 right parenthesis W e space k n o w space t h a t comma open parentheses x plus y close parentheses cubed equals x cubed plus y cubed plus 3 x y open parentheses x plus y close parentheses T h e r e f o r e comma space e q u a t i o n space left parenthesis 1 right parenthesis space b e c o m e s comma open parentheses a to the power of 1 third end exponent close parentheses cubed plus open parentheses b to the power of 1 third end exponent close parentheses cubed plus 3 a to the power of 1 third end exponent cross times b to the power of 1 third end exponent open parentheses a to the power of 1 third end exponent plus b to the power of 1 third end exponent close parentheses equals minus c rightwards double arrow a plus b plus 3 a to the power of 1 third end exponent cross times b to the power of 1 third end exponent open parentheses minus c to the power of 1 third end exponent close parentheses equals minus c rightwards double arrow a plus b plus c plus 3 a to the power of 1 third end exponent cross times b to the power of 1 third end exponent open parentheses minus c to the power of 1 third end exponent close parentheses equals 0 rightwards double arrow a plus b plus c equals 3 a to the power of 1 third end exponent cross times b to the power of 1 third end exponent cross times c to the power of 1 third end exponent rightwards double arrow a plus b plus c equals 3 open parentheses a to the power of 1 third end exponent cross times b to the power of 1 third end exponent cross times c to the power of 1 third end exponent close parentheses rightwards double arrow a plus b plus c equals 3 open parentheses a b c close parentheses to the power of 1 third end exponent rightwards double arrow open parentheses a plus b plus c close parentheses cubed equals 3 cubed open square brackets open parentheses a b c close parentheses to the power of 1 third end exponent close square brackets cubed rightwards double arrow open parentheses a plus b plus c close parentheses cubed equals 27 a b c

Answered by Vimala Ramamurthy | 1st Sep, 2014, 09:17: AM