Question

Question
The product of two consecutive positive integers is 42. Find the integers.

Answer 1

Answer: 6 and 7

Let x be the first integer.
Let (x + 1) be the next, consecutive integer.
Let P be the product.
P = x(x+1)
42 = x(x+1)
42 = x^2 + 1x
0 = x^2 + 1x -42
-6 times 7 = -42
-6 + 7 = 1
0 = (x + 7)(x -6)
x = -7 (inadmissible, integer has to be positive)
x = 6 (zero principle)
Next consecutive integer: 6 + 1 = 7
The integers are 6 and 7!