Question

For what value of n is n+1P3=nP4

Answer 1

n= P3 / (p2+1) (p+1) (p-1)

Answer 2

`n=(-p^(3) )/((1+p^(2))(1+p)(1-p) )`

Explanation:

To find the value of n we must solve the equation for n.

The equation can be written as:

`n + p^(3) = np^(4)\\`

We are going to move the terms with n to the left and the terms without n to the right:

`n + p^(3) = np^(4)\\n-np^(4) =-p^(3)`

Now we will proceed to factor the left side of the equation and solve for n:

`n-np^(4) =-p^(3)\\n(1-p^(4))=-p^(3)  \\n(1+p^(2))(1-p^(2) )=-p^(3) \\n(1+p^(2) )(1+p)(1-p)=-p^(3) \\n=(-p^(3) )/((1+p^(2))(1+p)(1-p) )`

Therefore
`n=(-p^(3) )/((1+p^(2))(1+p)(1-p) )`