Question

@mathstudent55
I think I'm doing this wrong

Answer 1

looks like sometimes true

Answer 2

\[\sqrt{x+4}+\sqrt{x+4}>4\]
-4 +4
____________________________
\[\sqrt{x+4} +\sqrt{x}>8\]
-4 -4
________________________
\[\sqrt{x} +\sqrt{x}>4\]

I think there's an error somewhere in there..
@mathstudent55

Answer 3

actually the first part is supposed to look like this:
sqroot x+4 + sqrt x-4 > 4
+4
my bad

Answer 4

You might want to consider the domain of this inequality. Is there a minimum value that x must have? a maximum one? Why or why not?

Just as you, Lilia, have attempted, I would try to solve this equality for x AFTER replacing the > sign with = . Yes, you can subtract 4 from the right side of the resulting equation, but no, you cannot subtract 4 from underneath the radical(s) of the left side.

One way of approaching the solution of this problem by trying to solve for x would involve: 1) Subtract Sqrt (x+4) from both sides of the equation.
2) Square both sides of the resulting equation.

Should you want to try this approach, please share your work here, so that someone else and/or i could give you feedback.

Answer 5

You can't subtract 4 from inside the square root sign.

Answer 6

Look at the second square root.

What is the smallest value of x you can use in it without making the inside of the square root negative?

Answer 7

Just look at this part for now.
What is the smallest x value that can be used?

Answer 8

1

Answer 9

1 - 4 = -3
You can't take the square root of -3, so 1 can't be used.

Answer 10

I've reconsidered, and would like to suggest an alternative approach:

Rule #1: You cannot, under most circumstances, have a negative number under the square root operator. Therefore, looking at Sqrt(x+4), x MUST be -4 or GREATER. Looking at Sqrt(x-4), x MUST be 4 or greater. Be certain you understand why; if you don't, ask for clarification.

Look at the following intervals: (-infinity,-4), (-4, 4), (4, infinity). On which of these intervals is the given expression defined? Your answer should help you to answer the problem at hand.

Answer 11

What values are allowed inside a sqaure root sign?

Answer 12

4, 8, 16

Answer 13

Yes, those values are allowed.
The answer is non-negative numbers.
Zero is ok, and positive numbers are ok.
Negative numbers can't be inside a square root sign.