Question 136
a) If $c\left(a^{3}+b^{3}\right)=a\left(b^{3}+c^{3}\right)=b\left(c^{3}+a^{3}\right)$ for positive real numbers $a, b, c$, does it necessarily follow that $a=b=c$?
b) If $a\left(a^{3}+b^{3}\right)=b\left(b^{3}+c^{3}\right)=c\left(c^{3}+a^{3}\right)$ for positive real numbers $a, b, c$, does it necessarily follow that $a=b=c$?
b) If $a\left(a^{3}+b^{3}\right)=b\left(b^{3}+c^{3}\right)=c\left(c^{3}+a^{3}\right)$ for positive real numbers $a, b, c$, does it necessarily follow that $a=b=c$?