Answer:
c = 13.
Explanation:
To find the two positive consecutive odd integers that have a product of 143, we can use the following steps:
Let x be the smaller odd integer, and x + 2 be the greater odd integer. This is because consecutive odd integers differ by 2.
Write an equation that relates x and x + 2 to the product of 143: x * (x + 2) = 143.
Simplify and solve for x: x^2 + 2x - 143 = 0. This is a quadratic equation that can be factored as (x + 13) * (x - 11) = 0.
Find the values of x that make the equation true: x = -13 or x = 11. Since we are looking for positive integers, we reject the negative solution and keep the positive one: x = 11.
Find the value of x + 2 by adding 2 to both sides of the equation: x + 2 = 13.
Check that the solution satisfies the original problem: 11 * 13 = 143, which is true.
Therefore, the two positive consecutive odd integers that have a product of 143 are 11 and 13. The greater integer is c = 13.