Question

x²+ y³ = z³ find solution​

Answer 1

Step-by-step explanation:

Solve for x:

One solution is:

x = 3√z³-y³

solve for y:

One solution is:

y = 3√z³-x³

solve for z:

One solution is:

z = 3√x³-y³

Actually because it’s a cubic equation there are two other solutions for x,y,z but that’s getting a little more complicated.

If you are looking for integer solutions, x,y,z = 0 is a trivial solution.

Another set of trivial solutions is where z = 0 and x + y = 0 or where x = 0 and z = y or where y = 0 and x = z.

However, as Leonhard Euler proved there are no solutions to x^3 + y^3 = z^3 where x,y,z are unique positive integers.

Update:

Fermet’s last theorem states that while there are unique positive integer solutions to a^n + b^n = c^n for n = 1 and n =2 there are no unique positive integer solutions for n >2.

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