The product of the three consecutive odd numbers is 1287. What is the sum of the largest and the smallest of the three numbers?

Correct option is C

Given:
Product of three consecutive odd numbers = 1287
Solution:
Let the three consecutive odd numbers be (x - 2), x, and (x + 2).
Their product is given by:
(x - 2) × x × (x + 2) = 1287
Using the identity (a - b)(a + b) = $$a^2 - b^2$$​, we get:
$$(x^2 - 4)$$​ × x = 1287
$$x^3$$​ - 4x = 1287
By observing the magnitude, we know that $$10^3$$​ = 1000 and $$11^3$$​ = 1331.
Let's test x = 11.
$$11^3$$​ - 4 × 11 = 1331 - 44 = 1287
So, the middle number x is 11.
The three consecutive odd numbers are 9, 11, and 13.
The smallest number is 9 and the largest number is 13.
Sum of the largest and smallest numbers = 9 + 13 = 22.
Final Answer
So the correct answer is (c)