Hello... I am Adnan from Bosnia... I am preparing for exam to be accepted in college ...
I need help for this problem...
Solve..
Thanks
Because we can see that an increase in degree does not change the value of the answer, we know that the variables MUST be something that always stays the same with changing whole number powers. Which could be or . But because a) the answer is (So it is obvious the variables cannot be zero), and b) the answer is ALWAYS 1, we know that the variables must be positive. (If they were negative they would switch between negative and positive between the square and cube functions, which they don't).
Using the above information, we can see that 1 variable must be 1, while the other two variables must be 0.
Suppose are the roots of a cubic equation
we have so the equation is
At the same time ,
so
The equation :
And
So
It is given that
Therefore ,
The equation is u^3 - u^2 = 0
u = 0 , 0, 1
Therefore , (x,y,z) = (0,0,1),(0,1,0),(1,0,0)
If the values of the right hand sides are not 1,the above method can be applied to solve it , It is not just used to prove the set of the solution is (0,0,1) in this case .