Finding the roots of simultaneous equations like these 
I am unable to find the answer to this question. It would also be helpful if you post what areas of mathematics this relates to. 

Expand $(a+b+c)^3$, giving
$$a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^3+3c^2b+3cb^2+6abc\\
=3(a^2+b^2+c^2)(a+b+c)-2(a^3+b^3+c^3)+6abc.$$
$$7^3=3\cdot35\cdot7-2\cdot151+6abc$$
$$abc=15.$$
