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system

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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
+40
+1

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