Question

The product of two consecutive numbers exceeds the square
of the smaller number by 20. Find the two numbers.

Answer 1

Answer:

20,21

Step-by-step 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.