can someone prove whether 2+2=5?

Question

can someone prove whether 2+2=5? if so, does this imply 2+2=4 is incorrect?

Answer 1

The short answer is you can't prove this statement because it is false... however if you are up for an invalid proof, you can "prove" most any falsehood. Here's one way to "prove" that 2+2 = 5.

Start with the identity:
-20 = -20

Express both sides in slightly different, yet equivalent ways:
16 - 36 = 25 - 45

Factor both sides:
4² - 4 * 9 = 5² - 5 * 9

Add the same thing to both sides:
4² - 4 * 9 + (81/4) = 5² - 5 * 9 + (81/4)

Factor both sides into perfect squares:
(4 - 9/2)² = (5 - 9/2)²

Take the square root of both sides:
4 - 9/2 = 5 - 9/2

Cancel the common term:
4 = 5

Replace 4 with 2+2
2 + 2 = 5

So can you find the mistake in the "proof"?

Answer 2

I read this some place, that 2+2=5 is only possible for extreme values of 2

when rounding up figures like 2.3 we say 2 and 2.5 or more than 2.5 we say 3

therefore if we take 2.3+2.3 still considered as 2 +2 we will get
4.6, which is also rounded up to be 5

hence high or extreme values of a number 2 can help u get an answer 5.

Answer 3

I agree with Puzzling. You can "prove" anything, but that doesn't mean it's true.

By the way, the mistake in his proof, is whenever you take the square root of both sides of an equation, you have to put in +/-.

At that line you have
(4-9/2)^2 = (5-9/2)^2
(-.5)^2 = (.5)^2

squaring both sides makes them true, without the square you have -.5 = +.5 which is false.

Answer 4

Hmm

Im assuming that you're overcomplicating your explanation to hide the flaw. Im pretty sure that its because the root can be negative or positive.

Following it literally, when you factorise to perfect squares, both sides equal 0.25, which is fine.

But square rooting them can equal the same if you take the negative root of the left hand side. ie -(4-9/2)=5-9/2

I still feel like thats not the full answer, but Im nearly there, right?