Find all solutions to the system a + b = 14 a^3 + b^3 = 812 + a^2 + b^2
convert first into \( b=14-a\)
then insert into second:
\(a^3+(14-a)^3=812+a^2+(14-a)^2\)
the end result is
\(a=\dfrac{35\pm2\sqrt{35}}{5}\)
insert a into first equation:
\(b=\dfrac{35\pm2\sqrt{35}}{5}\)
so \(\boxed{a,b=\dfrac{35\pm2\sqrt{35}}{5}}\)
