It has been a great many years since I did any algebra, now my son hits me with this:-

x squared + 2x = y find x and y

x squared + 2x = 48 find x

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- Feb 2nd 2010, 12:45 PMdivorce3My Son
It has been a great many years since I did any algebra, now my son hits me with this:-

x squared + 2x = y find x and y

x squared + 2x = 48 find x - Feb 2nd 2010, 01:05 PMArchie Meade
For the second one, you could write

$\displaystyle x^2+2x=48$

$\displaystyle x(x+2)=48$

The factors of 48 that differ by 2 are 6 and 8, so x=6

or -6 and -8 so x=-8 as that is 2 less than -6.

Or $\displaystyle x^2+2x-48=0$

$\displaystyle (x-a)(x-b)=x(x-b)-a(x-b)=x^2-bx-ax+ab=x^2-(a+b)x+ab$

We are looking for the factors of -48 that add to give 2,

these are -6 and 8, since

$\displaystyle (x-6)(x+8)=0$

Two values multiplied give zero means x-6=0 or x+8=0,

so x=6 or -8.

For the first one, you need more information, because you can take any x,

square it and add 2x and call the answer y. - Feb 2nd 2010, 01:17 PMpickslides
Well you can, but it is not advised.

You already have the answer for y

$\displaystyle x^2 + 2x = y$

$\displaystyle y = x^2 + 2x $

To solve for $\displaystyle x$ in the first equation you can say

$\displaystyle x^2 + 2x = y$

$\displaystyle x^2 + 2x - y=0$

by the quadratic formula

$\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)\times (-y)}}{2}$

This can be simplified to

$\displaystyle x = -1\pm\sqrt{1+y}$ - Feb 3rd 2010, 04:33 AMHallsofIvy
How is that different from just saying $\displaystyle y= x^2+ 2x$ for any value of x?