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# Algebra

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Find all solutions to the system

a + b = 14

a^3 + b^3 = 812 + ab

Nov 4, 2022

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Hi Guest!
Hint:

$$a^3+b^3=(a+b)(a^2+b^2-ab)=(a+b)((a+b)^2-2ab-ab)=(a+b)((a+b)^2-3ab)$$

Thus, $$a^3+b^3=14((14)^2-3ab)=14(196-3ab)$$

So:
$$\text{Given: }a^3+b^3 =812+ab \\ \implies 14(196-3ab)=812+ab$$

Now try to solve it from here :)

I hope this helps

Nov 4, 2022