can you please help me in proving this.....

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} \\ $.

#Algebra

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

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

Calvin Lin Staff - 4 years ago

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

Nikhil Raj - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$