word problem - quadratics

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Jul 12th 2008, 03:04 PM
dancingqueen9

word problem - quadratics

Aaaalright, apparently I'm supposed to solve this using the quadratic formula (ps: you dont have to run through the steps of the formula with me, i'm good with that part)

Here is the word problem: The sum of the squares of two consecutive numbers is 481. Find the integers.

How do I solve this?

Thank you :)
Jul 12th 2008, 03:44 PM
cyph1e

Let the smaller integer be $x$ , then the consecutive integer is $x+1$ . The sum of the squares of these numbers is 481, which leads us to the equation $x^2+(x+1)^2=481$ .
Jul 13th 2008, 08:53 AM
dancingqueen9

But then, won't it end up having a degree of 4? Is that still ok?
Jul 13th 2008, 09:36 AM
dancingqueen9

Oh, never mind. lol it does work
Jul 13th 2008, 10:00 AM
janvdl

Quote:

Originally Posted by cyph1e

Let the smaller integer be $x$ , then the consecutive integer is $x+1$ . The sum of the squares of these numbers is 481, which leads us to the equation $x^2+(x+1)^2=481$ .

Quote:

Originally Posted by dancingqueen9

But then, won't it end up having a degree of 4? Is that still ok?

Just to make sure you understand, let me build on cyph1e's foundation.

$x^2+(x+1)^2=481$

$x^2+(x^2 + 2x + 1) = 481$

$2x^2 + 2x + 1 =481$

$2x^2 + 2x - 480 = 0$

$2(x^2 + x - 240) = 0$

$2(x + 16)(x - 15) = 0$
Jul 13th 2008, 11:43 AM
cyph1e

Quote:

Originally Posted by janvdl

These numbers are not consecutive, although there squares do add up to 481. Their absolute values are consecutive though. (15 and 16)

(Unless I did something stupid again... (Wondering))

There are two solutions; $\left\{(15,16),(-16,-15)\right\}$ . The quadratic equation gives only the smaller integer $x$ , while the other consecutive integer of $x$ is $x+1$ .
Jul 13th 2008, 11:45 AM
janvdl

Quote:

Originally Posted by cyph1e

There are two solutions; $\left\{(15,16),(-16,-15)\right\}$ . The quadratic equation gives only the smaller integer $x$ , while the other consecutive integer of $x$ is $x+1$ .

Ah, of course you are correct! I knew I forgot something simple again. (Headbang)