Question

if x² + y²= z², then show x⁶ + y⁶ + 3x²y²z² = z⁶​

Answer 1

Hope this helps you

We just need to raise both sides to power of 3.

Answer 2

Answer:

x^2+y^2=z^2

x^6+y^6+3x^2y^2z^2

=(x^2)^3+(y^2)^3+3x^2y^2z^2

=(x^2+y^2)^3-3x^2y^2(x^2+y^2)+3x^2y^2z^2

putting, x^2+y^2=z^2 we get

(z^2)^3-3x^2y^2z^2+3x^2y^2z^2

=(z^2)^3

=z^6 (proved)