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Find all solutions to the system
a + b = 14
a^3 + b^3 = 812 + a^2 + b^2

 Nov 16, 2022
 #1
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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 \(\boxed{a,b=\dfrac{35\pm2\sqrt{35}}{5}}\)

 Nov 16, 2022

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