If $$k = (n + 2)(n - 2),$$ where $$n$$ is an integer value greater than $$2,$$ what is the value of $$k?$$

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If $$k = (n + 2)(n - 2),$$ where $$n$$ is an integer value greater than $$2,$$ what is the value of $$k?$$

by VJesus12 » Thu Sep 16, 2021 11:52 am

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If $$k = (n + 2)(n - 2),$$ where $$n$$ is an integer value greater than $$2,$$ what is the value of $$k?$$

(1) $$k$$ is the product of two primes
(2) $$k < 100$$

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Re: If $$k = (n + 2)(n - 2),$$ where $$n$$ is an integer value greater than $$2,$$ what is the value of $$k?$$

by swerve » Fri Sep 17, 2021 9:42 am

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VJesus12 wrote:
Thu Sep 16, 2021 11:52 am
If $$k = (n + 2)(n - 2),$$ where $$n$$ is an integer value greater than $$2,$$ what is the value of $$k?$$

(1) $$k$$ is the product of two primes
(2) $$k < 100$$

$$(n-2) \ast (n+2) = n^2 - 4$$
since $$k<100$$ we have $$96, 77, 60, 45, 32, 21, 12, 5$$ Not sufficient $$\Large{\color{red}\chi}$$
For (1); from the above list we have $$7\times 11, 7\times 3$$ in addition to possible numbers $$>100$$; hence, not sufficient $$\Large{\color{red}\chi}$$
(1) & (2) together we have $$77, 21$$ Not sufficient $$\Large{\color{red}\chi}$$