SOLUTION: If {{{x^2+y^2=85}}} and xy=5, what is the value of {{{(1/x-1/y)^2}}}? A) 5 B) 75 C) 80 D) 3

Algebra ->  Expressions -> SOLUTION: If {{{x^2+y^2=85}}} and xy=5, what is the value of {{{(1/x-1/y)^2}}}? A) 5 B) 75 C) 80 D) 3       Log On


   

Question 1043307: If x%5E2%2By%5E2=85 and xy=5, what is the value of %281%2Fx-1%2Fy%29%5E2?
A) 5
B) 75
C) 80
D) 3
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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If x%5E2%2By%5E2=85 and xy=5, what is the value of %281%2Fx-1%2Fy%29%5E2?
A) 5
B) 75
C) 80
D) 3
~~~~~~~~~~~~~~~~~ 

%281%2Fx-1%2Fy%29%5E2 = %28x-y%29%5E2%2F%28xy%29%5E2 = %28x%5E2+-+2xy+%2B+y%5E2%29%2F%28xy%29%5E2 = 

     replace x%5E2+%2B+y%5E2 by 85, and replace xy by 5. You will get

= %2885-2%2A5%29%2F5%5E2 = 75%2F25 = 3.

Answer.  3.  Option D).

Solved