• Jun 6th 2009, 07:51 PM
prettiestfriend
Why does
(2-X)^2=-1
have no real solution?
• Jun 6th 2009, 07:53 PM
Joel
This is because no number squared either positive or negative can give a negative answer.
• Jun 6th 2009, 08:10 PM
yeongil
And I'll be willing to bet that many math students, when seeing this problem, would expand the (2 - x)^2 and try to solve for x using the quadratic formula. It drives me nuts when students make problems much harder than they have to be.

01
• Jun 6th 2009, 09:40 PM
Prove It
Quote:

Originally Posted by yeongil
And I'll be willing to bet that many math students, when seeing this problem, would expand the (2 - x)^2 and try to solve for x using the quadratic formula. It drives me nuts when students make problems much harder than they have to be.

01

But that's not to say that doing that wouldn't work...

$(2 - x)^2 = -1$

$4 - 4x + x^2 = -1$

$x^2 - 4x + 5 = 0$

Now checking the discriminant gives...

$\Delta = (-4)^2 - 4\times 1\times 5$

$= 16 - 20$

$= -4 < 0$.

So no solution exists.

Having said that - you are right, it IS easiest to just notice that you can not square any real number to get a negative result.
• Jun 6th 2009, 10:22 PM
aidan
Quote:

Originally Posted by prettiestfriend
Why does
(2-X)^2=-1
have no real solution?

$(2-x)=i$
but that's no real solution.