Question

If a^1/3 + b^1/3 + c^1/3 = 0, then

पर्याय

• a + b + c = 0

• (a + b + c)³ =27abc

• a + b + c = 3abc

• a³ + b³ + c³ = 0

Answer 1

Given  `a^(1/3) +b^(1/3) +c^(1/3) = 0`

Using identity   `a^3 +b^3 +c^3 = 3abc` we get

Here    `a= a^(1/3) ,b=b^(1/3) , c = c^(1/3) `

`(a^(1/3))^3 + (b^(1/3))^3 +(c^(1/3))^3 = 3 xx a^(1/3) xx b^(1/3) xx c^(1/3)`

`(3sqrta)^3 +(3sqrtb)^3 +(3sqrtc)^3 =3 xx 3sqrta xx 3sqrtb xx3sqrt c`

`a+b+c = 3 xx 3sqrt a xx 3sqrtb xx 3sqrtc`

Taking Cube on both sides we get,

`(a+b+c)^3 = (3xx 3sqrta xx 3sqrtb xx 3sqrtc)^3`

`(a+b+c)^3 = 27abc` 

Hence the value of  `a^(1/3) +b^(1/3) +c^(1/3) = 0` is  `(a+b+c)^3 = 27abc` .