📘 algebra, linear algebra

1. Problem (i): Given that $\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = k$ (say), prove that $$\frac{x^3}{a^2} + \frac{y^3}{b^2} + \frac{z^3}{c^2} = \frac{(x+y+z)^3}{(a+b+c)^2}.$$ St