Question

Find two consecutive positive integers such that the square of the first decreased

by 17 equals 4 times the second​

Answer 1

Step-by-step explanation:

We let the numbers be x and x+ 1

Accordingly, x2-17= 4(x+1) will be our equation

Solve by first expanding the brackets, and then putting all terms to one side of the equation.

x2- 17 = 4x + 4

x2- 4x -17 - 4 = 0

x2- 4x - 21 = 0

This can be solved by factoring. Two numbers that multiply to -21 and add to - 4 are - 7and +3 thus,

(x -7) (x+ 3) =0

x=7 and - 3

However, since the problem says that the integers are positive, we can only take x = 7

Thus, the numbers are 7 and 8.

Hopefully this helps!