Question

an integer is one more than four times another. if the product of two integers is 39, then find the integers

Answer 1

sorry if its illegible, you can ask if its not clear

Answer 2

The integers are 3 and 13

Explanation:

Let the integers are x and y.

Then from the given directions we can frame two equations.

`x=4y+1.........(1)\\\\xy=39..........(2)\\\\`

From equation 2, the value of x is
`x=(39)/(y)`

On substituting this value in equation 1, we get

`(39)/(y)=4y+1\\4y^2+y-39=0`

Applying the quadratic formula, we get

`y_(1,\:2)=(-1\pm √(1^2-4\cdot \:4\left(-39\right)))/(2\cdot \:4)\\\\y=3,\:y=-(13)/(4)`

Among these two values, 3 is an integer.

Hence, y= 3

The value of x is x= 39/3 = 13

Therefore, the integers are 3 and 13