Question

Question:
What is the product of all integer values of x for which /x2(squared)-9/ is a prime number?

Answer 1

uh...

Answer 2

thats impossible to calculate i;m guesing

Answer 3

I am trying to understand WHAT the question is asking

Answer 4

The answer key says the answer is 64

Answer 5

is what you've written the exact wording of the question?

Answer 6

x could be any number and the prime number results of the equation could be infinite

Answer 7

It's not empty. Take x=4 @James.

Answer 8

yes thats the exact wording

Answer 9

MrM, yes.
\[ x^2−9 \] always has an integer factorization because
\[ x^2−9=(x−3)(x+3) \]
and these factors are not 1 when x > 4. So the only integer x such that x^2 - 9 is prime is when x = 4.

Answer 10

No odd number exists in the set

Answer 11

x=-4 also works

Answer 12

Try some even numbers

Answer 13

I was assuming that x^2 - 9 had to be positive, but perhaps not.

Answer 14

lol I have an arguement here for x=-4

Answer 15

So the product would be -16 then?

Answer 16

Prime number definition is that it should have only two factors one and itself but -4 having facctors -4 and -1 hahaha what do we do now????

Answer 17

does 64 work for that equation? the answer key says the answer is somehow 64

Answer 18

x^2-9 is still positive at x=-4.

Answer 19

yes, I'm trying to figure out how to recover 64.

Answer 20

it is 64 if you allow -2 and 2

Answer 21

right, and then you get negative values of x^2 - 9

Answer 22

but -5 usually is not defined as a prime number

Answer 23

usually they are natural numbers

Answer 24

But primes by definition are positive numbers, right?

Answer 25

yeah

Answer 26

Yes. But 64 would seem to imply that's what the question allows, which is unusual.

Answer 27

Yeah thats what i was also telling

Answer 28

there must be some range for the x values

Answer 29

If the set is {-4, -2, 2, 4}, then we have -4 x -2 x 2 x 4 = 64

Answer 30

Range is from [-9,infnty)

Answer 31

+4 and -4 make sense. +2 and -2 are unusual.

Answer 32

so what should i put for the answer?

Answer 33

I would use 4(-4)=-16

Answer 34

ok thanks for your time

Answer 35

I agree with Z.

Answer 36

I just noticed something...by /x2(squared)-9/ do you mean

\[|x^2-9|\]?

Answer 37

oh ... in that case ...

Answer 38

if that is the case then 64 is the answer

Answer 39

that is indeed the case

Answer 40

then -4,4,-2,2 all work

(-4)4(-2)2=64

Answer 41

Right. Then our concern about "negative prime" numbers goes away. The set of such x is

{-4, -2, 2, 4}

Answer 42

why does that matter?

Answer 43

because normally prime numbers are positive integers.

Answer 44

correct

Answer 45

@Zarkon: You're a problems solver, I would fan you twice if I could! :D

Answer 46

without the absolute value sign, then when x = 2 or x = -2, we have

\[ x^2 - 9 = -5 \]
which is not a positive integer and therefore can't be a prime.

Answer 47

but with the absolute value sign
\[ |x^2 - 9| = |-5| = 5 \]
when x = 2, -2

Answer 48

so how does it come out to be 64

Answer 49

we should post a sign at the beginning of the site that says don't use / /or \ \ for absolute value :)

Answer 50

ah yes sorry

Answer 51

We would need another site if we want to avoid wrong notations!