-x² + 4x + 5 = 0
(5 - x)( 1 + x) = 0
x = 5 or x = -1
We have to plug in the values back into the original problem to see if they fit. Lets try 5 first.
√[4(5) + 5] = 5.
√25 = 5. Five fits well. Lets try -1 to see if it is a fit
√[4(-1) + 5 = 1. We can simplify these now
√1 = 1. So one fits.
The solutions are non extraneous so Trisha is right.
4. I'm not really sure about this one but I think the question in other words means you should describe on which hill would have the greater length. I think the easiest way to find out would be to take a random number. Let's pick 6.
We would substitute 6 for x in both equations and see which equation would give us a greater value.
f(6) = 2(6)² + 5 = 77
g(6) = 2(6)² - 3(6) + 4 = 58
f(x) gives a greater value over g(x)
I would try to think of the 2nd one.
PS: You're not dumb. The answers are somewhere in your head. Have a great day.