the difference between the square of two consecutive odd number is 56 find the n...

September 2021 2 27 Report

the difference between the square of two consecutive odd number is 56 find the number

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

The two consecutive odd numbers are "13 and 15".

Step-by-step explanation:

Let the two consecutive odd number = x and (x + 2 )

To find, the numbers = ?

According to the question,

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

⇒ $x^2+4x+4-x^2=56$

⇒ $4x+4=56$

⇒ $4x=56-4=52$

⇒ $x=\dfrac{52}{4} =13$

∴ x + 2 = 13 + 2 = 15

Hence, the two consecutive odd numbers are 13 and 15.