| ebw said: I'm saying that "x = ±2" does not mean "both -2 and 2 are solutions". The "both -2 and 2 are solutions" interpretation is *inclusive*, in that it actively claims that -2 works. It is a common misconception that when you apply algebraic manipulations to solve an equation, you are creating solutions from the equations at hand. What I am saying is that the correct interpretation is *exclusive*, in other words "no number other than 2 or -2 is a solution". This makes no claim that -2 is a solution, only that -1 and 3 and uncountably many more numbers cannot be equal to x. But neither does it claim that -2 is NOT a solution. Starting from the assumption "x=2" and deducing that "x=±2" is not a contradiction (starting from "x=±2" and deducing that "x=2" would be flawed logic, but that is another discussion entirely). |
x = +/-2 is shorthand for +2 or -2, meaning they are both solutions. It's just the absolute value function f(x) = |x| where f(x) = 2, meaning -2 is indeed a solution for x. f(-2) = |-2| = 2.
I think you're more referring to what Jaydi said where x = 2 is not actually equivalent to x^2 = 4. The problem is, as I've repeated again and again that x = 2 is not a function. It's simply a declaration for the variable x as the value 2.
