Question

if a power 1/3 +b power 1/3 + c power 1/3 =0 . then show that (a+b+c )power 3 = 27 abc​

Answer 1

Answer:

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Step-by-step explanation:

a^1/3 + b^1/3 + c^1/3 = 0

a^1/3 + b^1/3 = - c^1/3 ---( 1 )

Do the cube of both sides of equation ( 1 ) we

get ,

( a^1/3 + b^1/3 )³ = ( - c^1/3 )³

(a^1/3)³+(b^1/3)³+3(a^1/3b^1/3 )(a^1/3 +b^1/3)= -c

a + b + 3a^1/3b^1/3( -c^1/3 ) = - c

a + b + c = 3( abc )^1/3

Do the cube both sides of the equation,

( a + b + c )³ = [ 3( abc )^1/3 ]³

( a + b + c )³ = 27abc