Ok so you are given; a, b, c are integers

abc = 729

and a + b + c = 91

Find a^2 + b^2 + c^2

How could I do this algebraically?

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- Nov 6th 2009, 05:10 PMacevipaTricky Problem
Ok so you are given; a, b, c are integers

abc = 729

and a + b + c = 91

Find a^2 + b^2 + c^2

How could I do this algebraically? - Nov 6th 2009, 05:32 PMWilmer
Hint: 1+9+81=91

- Nov 6th 2009, 05:59 PMBacteriusReply
Say $\displaystyle c = 1$. Therefore, we have :

$\displaystyle ab = 729$

$\displaystyle a + b = 90$

Substitute :

$\displaystyle a(90 - a) = 729$

$\displaystyle 90a - a^2 = 729$

$\displaystyle a^2 - 90a + 729 = 0$

Solve for $\displaystyle a$.

Facts for the lazy :

__Spoiler__:

And for the curious :

__Spoiler__:

Finding the sum of the squares shouldn't be too hard now ;) (remember $\displaystyle c = 1$)