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.
[tex]x=4y+1.........(1)\\\\xy=39..........(2)\\\\[/tex]
From equation 2, the value of x is [tex]x=\frac{39}{y}[/tex]
On substituting this value in equation 1, we get
[tex]\frac{39}{y}=4y+1\\4y^2+y-39=0[/tex]
Applying the quadratic formula, we get
[tex]y_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:4\left(-39\right)}}{2\cdot \:4}\\\\y=3,\:y=-\frac{13}{4}[/tex]
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
