Question

The product of two consecutive numbers exceeds the square

of the smaller number by 20. Find the two numbers.

Answer 1

20,21

Explanation:

Let x be the first number.

Let y be the 2nd number.

Given y - x = 1 (since they are consecutive)

Rearrange it: y = x+1 (equation 1)

Also given:

`xy-20=x^(2)` (equation 2)

Now we can substitute y = x + 1 into equation 2.

`x(x+1)-20 = x^(2) \\x^(2) +x-20 = x^(2) \\x-20=x^(2) -x^(2) \\x-20=0\\x=20`

Since we know x, the smaller number is 20, we can substitute to equation 1 to find y, the larger number.

y = 20+1

= 21.

Therefore the 2 numbers are 20 and 21.