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#1

$Old$ November 6th, 2009, 07:10 PM

acevipa $acevipa is offline$

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$Default$ Tricky 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?

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#2

$Old$ November 6th, 2009, 07:32 PM

Wilmer $Wilmer is offline$

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Hint: 1+9+81=91

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$Old$ November 6th, 2009, 07:59 PM

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Say $c = 1$ . Therefore, we have :

$ab = 729$
$a + b = 90$

Substitute :

$a(90 - a) = 729$
$90a - a^2 = 729$
$a^2 - 90a + 729 = 0$

Solve for $a$ .

Facts for the lazy :

Spoiler:

And for the curious :

Spoiler:

Finding the sum of the squares shouldn't be too hard now

(remember $c = 1$ )

Last edited by Bacterius; November 6th, 2009 at 08:31 PM.

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