xn+yn=zn

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Solution for xn+yn=zn equation:


Simplifying
xn + yn = zn

Solving
nx + ny = nz

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1nz' to each side of the equation.
nx + ny + -1nz = nz + -1nz

Combine like terms: nz + -1nz = 0
nx + ny + -1nz = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(x + y + -1z) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(x + y + -1z)' equal to zero and attempt to solve: Simplifying x + y + -1z = 0 Solving x + y + -1z = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x' to each side of the equation. x + y + -1x + -1z = 0 + -1x Reorder the terms: x + -1x + y + -1z = 0 + -1x Combine like terms: x + -1x = 0 0 + y + -1z = 0 + -1x y + -1z = 0 + -1x Remove the zero: y + -1z = -1x Add '-1y' to each side of the equation. y + -1y + -1z = -1x + -1y Combine like terms: y + -1y = 0 0 + -1z = -1x + -1y -1z = -1x + -1y Add 'z' to each side of the equation. -1z + z = -1x + -1y + z Combine like terms: -1z + z = 0 0 = -1x + -1y + z Simplifying 0 = -1x + -1y + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

n = {0}

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