Weird problem showed up on my math final today... help
so yah, i know that the final is over, but this question is really bugging me. It was an equation and i can normally do these. So the equation was:
square root of (x^2 + 5) = x - 5
Now, what i did was square both sides, and then i added like terms and such to get down to:
10x = 20, so naturally i thought x was 2, and that was one of the choices (multiple choice test) so i put down that it was 2. I had some time left at the end of the test, so i was checking over, and i plugged 2 back into the equation, and i got:
3 = -3, not 3 = 3 like i should have if it was the solution. So then what i did was, i put:
y = square root of (x^2 + 5) and
y = x - 5
into my calculator as two separate equations and graphed them to see where they intersected, (their intersection is a solution) and when i used the function on the calculator that finds the intersection, i got an error. So, another one of the solutions was no solution, so i changed it to that. I was just wondering if anyone knew why the answer i got algebraiclly doesn't work? i mean all my algebra and arithmetic are correct, so it doesn't make much sense.
Any help would be great!!