+0

# help me pls

0
108
2
+95

Let $$a, b,$$ and $$c$$ be distinct real numbers such that $$\frac{a^3 + 6}{a} = \frac{b^3 + 6}{b} = \frac{c^3 + 6}{c}.$$ Find $$a^3 + b^3 + c^3.$$

Sep 23, 2022

#1
+33338
+2

By inspection:

$$\frac{1^3+6}{1}=7$$

$$\frac{2^3+6}{2}=7$$

Unfortunately  $$\frac{3^3+6}{3}\ne7$$

However $$\frac{(-3)^3+6}{-3}=7$$

I'll leave you to finish.

Sep 23, 2022
#2
+95
0

tysm!!! the answer is -18 for anyone wondering :)

WorldEndSymphony  Sep 24, 2022