Question

AnswEr with proper Explanation.​

Answer 1

Answer:

c. 4

Step-by-step explanation:

Let k² = n² + 96 where n, k is a positive integerf

⇒ k² = n² + 96

⇒ k² - n² = 96

⇒ (k - n)(k + n) = 96

Both k, n must have the same parity. Hence we will try to find two factors of 96 such that both are even.

96 can be factorized as 2×48, 4×24, 6×16, 8×12

The smaller factor =k − n and the bigger factor =k + n

Hence, the values of (n, k) are (23,25),(10,14),(5,11),(2,10)

Hence, there are 4 possible values of n

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Answer 2

$\: \:$

Required Answer :-

$let \: \: k {}^{2} = n {}^{2} + 96$

(n, k is a positive integer)

$=> {k}^{2} - n {}^{2} = 96$

→ (k-n)(k+n) = 96

Here, both k and n must have the same parity

Factorization of 96 = 2×48,4×24,6×16,8×12

•°• The smaller factor = k-n

•°• The bigger factor = k+n

→ Values of (n,k) = (23,25) , (10,14) , (5,11) , (2,10)

•°• Total possible values = 4

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