Question

What is the sum of two consecutive odd numbers the difference of whose squares is 64?

Answer 1

Answer:

The sum of the required odd numbers is 32

Step-by-step explanation:

Let the consecutive odd numbers be: m and (m+2)

We are given that the difference in their squares is 64. Hence,

(m+2)^2 - m^2 = 64

(m+2+m)(m+2-m) = 64                 Using a^2 - b^2 = (a+b)(a-b)

(2m+2)(2) = 64

4(m+1) = 64

m+1 = 16

m=15

The odd numbers are: 15 and 17

The required sum is 15+17=32

Verify:

Difference of squares of 15 and 17 is 17^2 - 15^2 = 289-225=64