There are no solutions for z³ = x³ + y³ for a right triangle
How to determine the true statement?
The equation is given as:
z³ = x³ + y³
By Pythagoras theorem, we have:
z² = x² + y²
Multiply both sides by z
z³ = zx² + zy²
By comparing z³ = zx² + zy² and z³ = x³ + y³, we have:
x³ + y³ = zx² + zy²
Factor out z
x³ + y³ = z(x² + y²)
Make z the subject
z = (x³ + y³)/(x² + y²)
There exist no solution for the above equation
Hence, there are no solutions for z³ = x³ + y³ for a right triangle
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