Question

The difference between the squares of two consecutive odd numbers is 56 find the numbers

Answer 1

Answer:

13 and 15

Step-by-step explanation:

let one of the odd number be x

consecutive odd number will be x + 2

difference between them is 56

${(x + 2)}^{2} - {x}^{2} = 56 \\ {x }^{2} + 4 + 4x - {x}^{2} = 56 \\ \\ 4x + 4 = 56 \\ 4x = 56 - 4 \\ 4x = 52 \\ x = \frac{52}{4} \\ x = 13 \\ the \: other \: number \: \\ x + 2 = 13 + 2 = 15$

${13}^{2} = 169 \\ {15}^{2} = 225 \\ 225 - 169 = 56$

Answer 2

Answer:

13 and 15

Step-by-step explanation:

Let the numbers be x & x+2

According to the question-

(x+2)^2 - x^2=56

(x+2+x)(x+2-x)=56

(2x+2) * 2=56

2x+2=28

2x=26

x=13

x+2=15

the numbers are 13 and 15.