Question

(iii) The difference between the squares of two consecutive odd numbers is 56. Find the numbers​

Answer 1

Answer:

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

Answer 2

Answer:

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

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)

2

−x

2

=56

⇒ x^2+4x+4-x^2=56x

2

+4x+4−x

2

=56

⇒ 4x+4=564x+4=56

⇒ 4x=56-4=524x=56−4=52

⇒ x=\dfrac{52}{4} =13x=

4

52

=13

∴ x + 2 = 13 + 2 = 15

Explanation:

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