Question

Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.

Answer 1

Answer:

The two consecutive positive integers are 7 and 8

Step-by-step explanation:

Let

x ----> the first positive integer

x+1 ----> the second consecutive positive integer

we know that

$x^{2} -17=4(x+1)$

Solve for x

$x^{2} -17=4x+4\\ \\x^{2}-4x-21=0$

Solve the quadratic equation by graphing

The solution is x=7

see the attached figure

Find the value of x+1

x+1=7+1=8

therefore

The two consecutive positive integers are 7 and 8