So, as you can see in the photo above, I solved this equation and I got 2 results as an answer. Both of which seem correct to me. But my teacher stated that the -2 solution is incorrect, and that 1 is the only correct answer. I graphed the function, in a software, and I saw that the function really does only cut the x axis at 1 and that the function is only defined at x greater or equal to 2. With all of that being stated, what I don't understand is: why -2 isn't a solution and why the function is only defined at x greater or equal to 2.
P.S. In case that you are wondering, Solución means solution in Spanish.
Best Answer
I think the key idea here is to be careful when squaring both sides of an equation.
Any solution for an equation $L(x) = R(x)$ is surely also a solution for $(L(x))^2$ = $(R(x))^2$, but the reverse is not necessarily true.
If $x$ satisfies $(L(x))^2 = (R(x))^2$ then we can only deduce that $|L(x)| = |R(x)|$, but after taking away the absolute value signs around each side, the equality might not hold (the signs of either side may not match).
You found 2 candidate solutions from the squared equation but you need to check them in the original equation to make sure they still work on the "un-squared expressions".