Question

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?

Answer 1

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