The square of one number is 23 less than the square of a second number. If the second number is 1 more than the first, what are the two numbers?

Step-by-step explanation:

The numbers are 11 & 12

Explanation:

Let the first number be f and the second |number be s

Now the square of first No. is 23 less than the square of second No.

ie.  f 2 + 23 = s 2 . . . . . (1)

The second No. is 1 more than the first

ie  f + 1 = s  . . . . . . . . . . .(2)

squaring (2), we get

( f + 1 ) 2 = s 2

expanding

f 2 + 2 ⋅ f + 1 = s 2  . . . . . (3)

Now (3) - (1) gives

2 ⋅ f − 22 = 0

or  

2 ⋅ f = 22

thus,  f = 22 2 = 11

and  s = f + 1 = 11 + 1

=

12

So the numbers are 11 & 12

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