Question 1169576

Find all solutions to the system

a + b = 14
a^3 + b^3 = 812.

How would I solve this? (Not looking for an answer by the way)
<pre>a + b = 14 ----- eq (i)
{{{matrix(3,3, (a + b)^2, "=", 14^2, a^2 + 2ab + b^2, "=", 196, a^2 + b^2, "=", 196 - 2ab)}}} ---- Squaring eq (1) ---- eq (ii)
{{{matrix(1,3, a^3 + b^3, "=", 812)}}}
{{{matrix(1,3, (a + b)(a^2 - ab + b^2), "=", 812)}}} ----- eq (iii)
(14)(196 - 2ab - ab) = 812 ----- Substituting 14 for a + b, and 196 - 2ab for {{{a^2 + b^2}}} in eq (iii)  
Can you now take it from here? You now know what a + b equals, and from above, what ab is!