Question 980977
(px + 1/x)^n is 5/2
<pre>
The 4th term is 

{{{(matrix(2,1,n,3))(px)^(n-3)*(1/x)^3}}}{{{""=""}}}{{{20*p^(n-3)x^(n-3)*(1/x^3)}}}{{{""=""}}}{{{20*p^(n-3)*x^(n-6)}}}{{{""=""}}}{{{5/2}}}

So {{{20*p^(n-3)*x^(n-6)}}}{{{""=""}}}{{{5/2}}} must be true for all x&#8800;0

Therefore the power of x must be 0, or n-6=0, or n=6

{{{20*p^(6-3)*x^(6-6)}}}{{{""=""}}}{{{5/2}}}

{{{20*p^3*x^0}}}{{{""=""}}}{{{5/2}}}

{{{20*p^3*1}}}{{{""=""}}}{{{5/2}}}

{{{20*p^3}}}{{{""=""}}}{{{5/2}}}

Multiply both sides by 2

{{{40*p^3}}}{{{""=""}}}{{{5}}}

Divide both sides by 5

{{{8*p^3}}}{{{""=""}}}{{{1}}}

{{{p^3}}}{{{""=""}}}{{{1/8}}}

{{{p}}}{{{""=""}}}{{{1/2}}}

Edwin</pre>