Question

What is wrong with this proof:

;)

Answer 1

\[(4-\frac{9}{2})^{2} \]
\[(4)^{2} - (2)(4)(\frac{9}{2}) + (\frac{9}{2})^{2}\]

\[16 - 36 + (\frac{9}{2})^{2}\]

\[-20 + (\frac{9}{2})^{2}\]

\[25 - 45 + (\frac{9}{2})^{2}\]

\[(5)^{2} - (2)(5)(\frac{9}{2}) + (\frac{9}{2})^{2}\]

\[(5-\frac{9}{2})^{2}\]

Answer 2

So based on what I wrote above:

\[\sqrt{(4-\frac{9}{2})^2} = \sqrt{(5-\frac{9}{2})^{2}}\]
simplify that to get
\[4 - \frac{9}{2} = 5 - \frac{9}{2}\]
and
4 = 5
voila

Answer 3

I know whats wrong with this proof. It EXISTS.

Answer 4

@Gdeinward
Does \(\sqrt{4-\frac{9}{2}}\) really exist?

Answer 5

Also when you take the square root there is a ±.

Answer 6

justjm is already getting on it, but I'll re-iterate

(4 - 9/2)^2 = (5 - 9/2)^2 is a true statement

the left side is equal to (-0.5)^2 and the right side is equal to (0.5)^2
of course, when you take the square root, as justjm stated, you must take into consideration the positive and negative solutions of the square root.

Answer 7

\(\sqrt{ \left (4-\frac{9}{2} \right )^2} = \left( \sqrt{(4-\frac{9}{2}} ~~\right) ^2\)

!!!!

Nothing to do w/ PEDMAS.