SOLUTION: Given that the fourth term in the expansion of (px + 1/x)^n is 5/2 . find the values of n and p, where n is positive integer.

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Question 980977: Given that the fourth term in the expansion of (px + 1/x)^n is 5/2 . find the values of n and p, where n is positive integer.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
(px + 1/x)^n is 5/2
The 4th term is 

%28matrix%282%2C1%2Cn%2C3%29%29%28px%29%5E%28n-3%29%2A%281%2Fx%29%5E3%22%22=%22%2220%2Ap%5E%28n-3%29x%5E%28n-3%29%2A%281%2Fx%5E3%29%22%22=%22%2220%2Ap%5E%28n-3%29%2Ax%5E%28n-6%29%22%22=%22%225%2F2

So 20%2Ap%5E%28n-3%29%2Ax%5E%28n-6%29%22%22=%22%225%2F2 must be true for all x≠0

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

20%2Ap%5E%286-3%29%2Ax%5E%286-6%29%22%22=%22%225%2F2

20%2Ap%5E3%2Ax%5E0%22%22=%22%225%2F2

20%2Ap%5E3%2A1%22%22=%22%225%2F2

20%2Ap%5E3%22%22=%22%225%2F2

Multiply both sides by 2

40%2Ap%5E3%22%22=%22%225

Divide both sides by 5

8%2Ap%5E3%22%22=%22%221

p%5E3%22%22=%22%221%2F8

p%22%22=%22%221%2F2

Edwin