Everything is OK until after this step:
(2 + 2 - 9/2)2 = (5 - 9/2)2
Note that the quantity inside the parenthesis on the left is actually -1/2 , while on the right, the quantity inside the parentheses is 1/2. And when we square both, we get the same result = 1/4.
But, in the next to the last step, we've taken the negative square root of 1/4 on the left, while on the right, we've taken the positive square root. Thus, the two sides always differ by 1. Thus, it appears that 4 = 5.
To see this more clearly, note that
(7 - 3)2 = (3 - 7)2
(-4)2 = (4)2 → (16) = (16)
But, if I stealthily take the negative root of 16 on the left and the positive root on the right, then we could claim that:
-4 = 4
Which clearly isn't true.......It also proves that we need to be careful when squaring things in an equation.....the square of one side might equal the other, but the original quantities might not.....
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+130511 