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`        Find x^1/3 + y^1/3 + z^1/3 = 0Then find (x + y + z)^3`
3 years ago

Arun Kumar
IIT Delhi
256 Points
```
Hello Student
$\\Let x^{1/3} = a, y^{1/3} = b, z^{1/3} = c \\The question then becomes, if (a+b+c) = 0 \\ then what is the value of (a^3+b^3+c^3)^3. \\We have a+b = -c. \\=> (a+b)^3 = (-c)^3 = -c^3. \\=> a^3+b^3+3*a*(b^2)+3*(a^2)*b = -c^3 \\=> a^3+b^3+c^3 = -{ 3*a*(b^2)+3*(a^2)*b } = -3*a*b*(a+b) = -3*a*b*(-c) = 3abc. \\=> (a^3+b^3+c^3)^3 = (3abc)^3 = 27(a^3)(b^3)(c^3) = 27xyz.$
Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty

```
3 years ago
Pallavi Das
17 Points
```										we know if a+b+c=0 then a^3+b^3+c^3=3abcso ifx^1/3 + y^1/3 + z^1/3 = 0 thenx+y+z=3.x^1/3.y^1/3.z^1/3so (x+y+z)^3=(3.x^1/3.y^1/3.z^1/3)^3(x+y+z)^3=27xyz
```
3 years ago
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