SOLUTION: Assuming that the variables are nonzero, when will the sum of c and d be equal to the sum of the reciprocals of c ad d? Translation: (variables are nonzero) c + d = 1/c + 1/d

Algebra ->  Expressions-with-variables -> SOLUTION: Assuming that the variables are nonzero, when will the sum of c and d be equal to the sum of the reciprocals of c ad d? Translation: (variables are nonzero) c + d = 1/c + 1/d       Log On


   



Question 775255: Assuming that the variables are nonzero, when will the sum of c and d be equal to the sum of the reciprocals of c ad d?
Translation: (variables are nonzero) c + d = 1/c + 1/d
Answer: ?
I was right in the translation part, but I got wrong in the answer. I answered "it will be equal when we also get the reciprocal of c + d" which did not make any sense at all. I wonder if the right answer is "if c and d are 1, then they will also be equal to the reciprocals." but I am not really sure.
Thank you! :)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

c+%2B+d+=+1%2Fc+%2B+1%2Fd+
c+%2B+d+=+d%2Fcd+%2B+c%2Fcd
c+%2B+d+=+%28d%2B+c%29%2Fcd+
cd=+%28d%2B+c%29%2F%28+c+%2B+d+%29
cd=+1
so, only if c+=+1, d+=+1 or c+=+-1, d+=+-1, cd will be equal to +1+, and c+%2B+d+=+1%2Fc+%2B+1%2Fd+