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

Answer:

The integers are 3 and 13

Step-by-step 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 $x=\frac{39}{y}$

On substituting this value in equation 1, we get

$\frac{39}{y}=4y+1\\4y^2+y-39=0$

Applying the quadratic formula, we get

$y_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:4\left(-39\right)}}{2\cdot \:4}\\\\y=3,\:y=-\frac{13}{4}$

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