Question

Help!!!!

Answer 1

\[x^{2} \ge 17\]

Answer 2

\[x^2-17\ge0\]

Answer 3

\[(x-\sqrt{17})(x+\sqrt{17})\ge0\]

Answer 4

Can you take it from there?

Answer 5

Can you help me go through it please. I'm having difficulty w/ problems like this :(

Answer 6

For the product to be greater than 0, both factors have to be positive or both factors have to be negative. Do you understand that?

Answer 7

no sorry

Answer 8

6(3) How many factors is that?

Answer 9

2

Answer 10

Are they both positive?

Answer 11

yes because bot numbers are positie

Answer 12

positive

Answer 13

Is the answer positive or negative?

Answer 14

positive

Answer 15

So I could write that :
\[6(3)\ge 0\]

Answer 16

Would you agree?

Answer 17

yes

Answer 18

Also if both of my factors are negative as in
(-6)(-3)

Answer 19

I would again get a positive answer and could write that:
\[(-6)(-3)\ge0\]

Answer 20

However is one factor is negative and one positive as in: (-6)(3) or (6)(-3) then I could not truthfully write:
\[(-6)(3)\ge0\]

Answer 21

So back to your problem. If
\[(x-\sqrt{17})(x+\sqrt{17}\ge0\]

Answer 22

If that is true then both factors have to be negative or both factors have to be positive. Do you see that now?

Answer 23

kinda. so the answer should be \[\times \ge 17\]

Answer 24

So the usual technique is to draw a picture of each factor indicating where each is positive and each is negative.