If m and n are whole numbers and mn= 196, what is the value of (m - 3)(n+1)?a)2744b)1c)121d)1331Correct answer is option 'D'. Can you explain this answer?

Question

Answer

To find the value of (m - 3)(n + 1), we need to find the values of m and n.

Given that mn = 196, we know that m and n are factors of 196.

Finding the factors of 196, we have:
1 x 196
2 x 98
4 x 49
7 x 28
14 x 14

Since m and n are whole numbers, we can eliminate the factor pairs that include fractions or decimals.

Therefore, the possible values for m and n are:
m = 1, n = 196
m = 2, n = 98
m = 4, n = 49
m = 7, n = 28
m = 14, n = 14

Now, let's substitute these values into (m - 3)(n + 1) and find the result for each case:

For m = 1, n = 196:
(1 - 3)(196 + 1) = (-2)(197) = -394

For m = 2, n = 98:
(2 - 3)(98 + 1) = (-1)(99) = -99

For m = 4, n = 49:
(4 - 3)(49 + 1) = (1)(50) = 50

For m = 7, n = 28:
(7 - 3)(28 + 1) = (4)(29) = 116

For m = 14, n = 14:
(14 - 3)(14 + 1) = (11)(15) = 165

Out of these values, the only one that matches the correct answer choice of 1331 is when m = 14 and n = 14.

Therefore, the value of (m - 3)(n + 1) is 1331, which is option D.

Answer

mⁿ = 196

We know that 14² = 196

Hence we can take m = 14 and n = 2

(m - 3)⁽ⁿ⁺¹⁾ = (14 - 3)⁽²⁺¹⁾ = 11³ = 1331

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