This is ok because both sides evaluate to 1/4.
It's what happens next that is not correct.
If you just square root both sides you get
and that is not correct. It's the careless square rooting that causes the false result.
Because a square root can be + or - the equation is valid if one of the signs is changed.
Take it as a warning not to square root without thinking about what is happening.
Calculators will only give a positive square root because they are programmed to give a single answer. Some people regard the root sign as meaning this which is fine. But it's always worth thinking about the negative case, because that might give the answer you want.
Bob
]]>None of these are correct.
Am I on the right track?
]]>Now the error is obvious. Every number has two square roots, so you have to take care when using 'rooting' in an algebraic manipulation.
Bob
]]>(4 - 9/2) ² = (5 - 9/2) ²
4 = 5
]]>
-20=-20
16-36 = 25-45
4 ² - 9*4 = 5 ² - 9*5
4 ² - 9*4 + 81/4 = 5 ² - 9*5 + 81/4
(4 - 9/2) ² = (5 - 9/2) ²
4 = 5
4 + 0 = 4 + 1
0 = 1