Can the Brilliant community help me proving this. If $$\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c} \\ show, \dfrac{x^3 +a^3}{x^2 + a^2} + \dfrac{y^3 + b^3}{y^2 + b^2} + \dfrac{z^3 + c^3}{z^2 + c^2} = \dfrac{(x + y + z)^3 + (a + b + c)^3}{(x + y + z)^2 + (a + b + c)^2} \\$$.

Note by Nikhil Raj
1 year, 1 month ago

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What happens if you substitute in $$x = ka, y = kb, z = kc$$ ?

Staff - 1 year, 1 month ago

Thanks, I got the answer. I have got more questions which i will post after some while.

- 1 year, 1 month ago