Question

The difference between the squares of two consecutive numbers is 37. Find the numbers.​

Answer 1

ANSWER:

• The numbers are 18, 19.

GIVEN:

• The difference between the squares of two consecutive numbers is 37.

TO FIND:

• The two consecutive numbers.

EXPLANATION:

Let the numbers be x, x + 1 [ Difference between, two consecutive numbers is 1 ]

(x + 1)² - x² = 37

$\boxed{\bold{\large{\gray{(A + B)^2=A^2 + 2AB + B^2}}}}$

x² + 2(x)(1) + 1² - x² = 37

x² + 2x + 1 - x² = 37

2x + 1 = 37

2x = 36

x = 18

x + 1 = 19

HENCE THE NUMBERS ARE 18, 19.

VERIFICATION:

(x + 1)² - x² = 37

Substitute x = 18, x + 1 = 19.

19² - 18² = 37

361 - 324 = 37

37 = 37

HENCE VERIFIED.

EXTRA POINTS:

For consecutive odd numbers:

• For consecutive odd numbers the unknown numbers will be taken as 2x + 1 , 2x + 3.

• We know that 2x will always even, therefore 2x + 1 and 2x + 3 will be always be odd.

For consecutive even numbers:

• For consecutive even numbers the unknown numbers will be taken as 2x , 2x + 2.

• We know that 2x will always even, therefore 2x and 2x + 2 will be always be even.