Question

The difference between the squares of two consecutive odd number is 56 find the number 2. The difference between the square of two consecutive even number is 36 find the numbers

Answer 1

Answer:

1. 13 and 15 2. Take the two numbers as 2x and 2x + 2 and follow the same procedure as 1

Step-by-step explanation:

1.

Let 2x+1 be a odd number and 2x+3 is the next odd number.

Then, ATQ,

(2x+3)² - (2x+1)² = 56

⇒ (4x² + 12x + 9) - (4x² +4x +1) = 56

⇒ 12x - 4x + 9 - 1 = 56

⇒ 8x+8 = 56

⇒ x+1 = 56/8 = 7

⇒ x= 7-1 = 6

∴ the two consecutive odd numbers are 2x + 1 = 2 × 6 +1 =13 and 2x +3 = 2 × 6 +3 =15

2. take the two consecutive even numbers to be 2x and 2x +2 and follow the same procedure as 1.