Question

If m, n belongs to N and m^2-n^2=13,then (m+1)(n+1)is equal to

Answer 1

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Answer 2

Answer:

56

Step-by-step explanation:

Given,

m and n are natural numbers,

Such that,

$m^2-n^2=13$

$\implies (m+n)(m-n) = 13\times 1$ ( Because, 13 is a prime number and the sum or subtraction of two natural numbers can not be a fraction )

Also, for natural numbers,

m + n > m - n

Thus, m + n = 13 and m - n = 1,

By solving these equations,

We get, m = 7 and n = 6,

Now,

$(m+1)(n+1) = mn + m + n + 1 = 7\times 6 + 7 + 6 + 1 = 42 + 14 = 56$