@Active-Forumer
It's a trick. The first error already occurs in the second equal sign.
4 - 9/2 = 4 - 4.5 = - 0.5 = - 1/2
That's negative. However, they replace 4 - 9/2 with √((4 - 9/2)^2). That's wrong, because the latter is positive. Let me show you:
√((4 - 9/2)^2) = √((- 1/2)^2) = √(- (- 1/4)) = √(+ 1/4) = + 1/2
That's positive.
Crucially, the difference between the two terms is
√((4 - 9/2)^2) - (4 - 9/2) = 1/2 - (- 1/2) = 1/2 + 1/2 = 1
So it's no coincidence that the original 4 becomes a 5. They sneakily (and erroneously) added a hidden 1 to the right hand side of the equation.
No magic, just mathematical trickery.
Edit: The rest of the calculation is correct. √((4 - 9/2)^2) and √((5 - 9/2)^2) are actually both equal to +1/2.
This might seem surprising at first, but remember that numbers have many different looking representations.
1/2, 0.5, 0.49 (9 repeating), √((4 - 9/2)^2), √((5 - 9/2)^2), (√3)*sin(60º), etc.
These are just some of the representations of the number one half.
@Active-Forumer
It's a trick. The first error already occurs in the second equal sign.
4 - 9/2 = 4 - 4.5 = - 0.5 = - 1/2
That's negative. However, they replace 4 - 9/2 with √((4 - 9/2)^2). That's wrong, because the latter is positive. Let me show you:
√((4 - 9/2)^2) = √((- 1/2)^2) = √(- (- 1/4)) = √(+ 1/4) = + 1/2
That's positive.
Crucially, the difference between the two terms is
√((4 - 9/2)^2) - (4 - 9/2) = 1/2 - (- 1/2) = 1/2 + 1/2 = 1
So it's no coincidence that the original 4 becomes a 5. They sneakily (and erroneously) added a hidden 1 to the right hand side of the equation.
No magic, just mathematical trickery.
Edit: The rest of the calculation is correct. √((4 - 9/2)^2) and √((5 - 9/2)^2) are actually both equal to +1/2.
This might seem surprising at first, but remember that numbers have many different looking representations.
1/2, 0.5, 0.49 (9 repeating), √((4 - 9/2)^2), √((5 - 9/2)^2), (√3)*sin(60º), etc.
These are just some of the representations of the number one half.