1. ## 2*2=5

how 2*2 can be equal to 5?

2. ## 2*2

-20=-20
16-36=25-45
We add 81/4 to sides of equation:
16-36+81/4=25-45+81/4
42-2*4*9/2+(9/2)2=52-2*5*9/2+(9/2)2
(22-9/2)2=(5-9/2)2
Square root of sides:
2*2-9/2=5-9/2
2*2=5
but why the result is this?

3. Hello afsaneh
Originally Posted by afsaneh
-20=-20
16-36=25-45
We add 81/4 to sides of equation:
16-36+81/4=25-45+81/4
42-2*4*9/2+(9/2)2=52-2*5*9/2+(9/2)2
(22-9/2)2=(5-9/2)2
Square root of sides:
2*2-9/2=5-9/2
2*2=5
but why the result is this?
It's when you take the square root that you need to be careful. Just because $a^2 = b^2$, it doesn't necessarily mean that $a = b$. It could be that $a = -b$.

It is true that $(2^2-\tfrac92)^2 = (5 - \tfrac92)^2$, the line I've coloured
red. This is because, when we evaluate the expressions in each bracket, the one on the LHS is $-\tfrac12$ and the one on the RHS is $\tfrac12$. Squaring each of these gives the same answer: $\tfrac14$. But that doesn't mean that they are equal, does it?

So remember: when you take a square root, remember the possible minus sign!