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

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

Grade:11

3 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student


Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty
Pallavi Das
17 Points
9 years ago
we know if a+b+c=0 then a^3+b^3+c^3=3abc
so ifx^1/3 + y^1/3 + z^1/3 = 0 then
x+y+z=3.x^1/3.y^1/3.z^1/3
so (x+y+z)^3=(3.x^1/3.y^1/3.z^1/3)^3
(x+y+z)^3=27xyz
 
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

we know if a + b + c = 0 then
a^3 + b^3 + c^3 = 3abc
so if x^1/3 + y^1/3 + z^1/3 = 0 then
x + y + z = 3.x^1/3.y^1/3.z^1/3
so ( x + y + z )^3 = (3.x^1/3.y^1/3.z^1/3)^3
(x+y+z)^3 = 27xyz

Thanks and Regards

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