Is 4=5? (See below)?

Question

Theorem: 4 = 5
Proof:
-20 = -20
16 - 36 = 25 - 45
4^2 – 9x4 = 5^2 – 9x5
4^2 – 9x4 + 81/4 = 5^2 – 9x5 + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2
4 = 5




and don't tell me it doesn't work. It does.

I did not distribute anything. FOIL (4 - 9/2)^2 and you get 4^2 – 9x4 + 81/4. FOIL (5 - 9/2)^2 and you get 5^2 – 9x5 + 81/4

Answer 1

You can't use the distributive property on exponents (like you have in step 4). This does not work.

Answer 2

The first answer was right, you can't use the distributive property on exponents. Here's an example:
3^2 + 4^2 =
9+16 =
25

Whereas:
(3 + 4)^2 =
7^2 =
49

Does 25 = 49? I think not.

P.S. If you don't want us to tell you it doesn't work, why did you post this question?

Answer 3

When you square a negative number you get the same value as when you square a positive number. 4-9/2 does not equal 5-9/2 one is a negative .5 the other is a positive .5. The absolute magnitude of the two is the same.

Answer 4

The theorem is false. To start what ever you do to one side of "=" you must do same to other. further so nether (4-9/2)^2=(5-9/2)^2 and 4-9/2=5-9/2 are true. Remember you must do multiplication and division first.

4-9/2=-.5
5-9/2=.5

Answer 5

The fact that the squares of two expressions are equal does not mean that the expressions themselves are equal--they may have opposite signs.

That is the case here. (4-9/2) is -1/2, while (5-9/2) is +1/2. Their squares are equal, but you can't take the square root and expect the equality to hold. Your proof becomes false two lines from the bottom.

Answer 6

(4-9/2) is the negative square root of (4-9/2)^2, while (5-9/2) is the positive square root of (5-9/2)^2. You either have to take the positive square root of both sides or the negative square root of both sides. If you take the negative square root of both sides, you get 4-9/2 = 9/2-5, and if you take the positive square root of both sides, you get 9/2-4 = 5-9/2.

Answer 7

Good catch Michael. I knew it had to be something simple.

(4 - 9/2)^2 = (5 - 9/2)^2 is true, but

(4 - 9/2) = (5 - 9/2) is not

I'll have to remember that one. It draws you into the upper part where the calculations are more tricky, but you can just skip that section.

It's easier to see when you write it in decimals.

(4 - 9/2)^2 = (5 - 9/2)^2
(4 - 4.5)^2 = (5 - 4.5)^2
-0.5^2 = 0.5^2
0.25 = 0.25

Answer 8

The method you used to prove 4=5 is similar to what is mentioned below:

(4)^2 = (-4) ^2
& so 4 = -4

But this is not true since equality cannot be applied to squares...

Hope this makes clear that your proof is wrong

Answer 9

I haven't seen this one before. I have to say that it's rather cleaver.

Mistake is when
(4 - 9/2)^2 = (5 - 9/2)^2
Becomes
4 - 9/2 = 5 - 9/2
When it really should become
+/- (4 - 9/2) = +/- (5 - 9/2)
+/- 0.5 = +/- 0.5

Answer 10

Ask Emmanuel Goldstein.