Question

The sum of two consecutive natural number is 23 . Find the difference between the squares of such two number?

Answer 1

Answer:

Suppose that first consecutive natural number is x.

then, the second consecutive natural number is( 23-x)

A .T .Q,

x² -(23-x)² =0

x²- (529 +x² -46x) =0

x²-529-x²+46x =0

-529+46x =0

46x=529

x =529/46

x= 23/2

hence the first consecutive natural number is 23/2

and second consecutive natural number is (23-23/2)

=23/2.

Answer 2

Let the first number be x, then the consecutive natural number will be x+1.

x + x + 1 = 23

2x + 1 =23

2x = 23 - 1 =22

x = 22/2 = 11

x + 1 = 11 + 1 = 12

The numbers are 11 and 12.

Difference between squares of these numbers = 12² - 11² = 144 - 121 = 23 is the answer.