SOLUTION: If p+q=n and {{{1/p +1/q =m}}}, where p and q are positive, find {{{(p-q)^2}}}.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If p+q=n and {{{1/p +1/q =m}}}, where p and q are positive, find {{{(p-q)^2}}}.      Log On


   



Question 1114796: If p+q=n and 1%2Fp+%2B1%2Fq+=m, where p and q are positive, find %28p-q%29%5E2.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given

p + q = n,

m = 1%2Fp+%2B+1%2Fq = %28q%2Bp%29%2F%28pq%29 = n%2Fpq%29,   (  <<<---=== I replaced p+q in the numerator by n, since it is given !  )


which implies  pq = n/m.


Then  %28p-q%29%5E2 = %28p%2Bq%29%5E2+-+4pq = n%5E2-4%2A%28n%2Fm%29.


Answer.  Then  %28p-q%29%5E2 = n%5E2-4%2A%28n%2Fm%29.

Solved.