Why does
(2-X)^2=-1
have no real solution?

2. This is because no number squared either positive or negative can give a negative answer.

3. 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

4. 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...

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

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

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

Now checking the discriminant gives...

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

$\displaystyle = 16 - 20$

$\displaystyle = -4 < 0$.

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.

5. Originally Posted by prettiestfriend
Why does
(2-X)^2=-1
have no real solution?
$\displaystyle (2-x)=i$
but that's no real solution.