SOLUTION: The reciprocal of the square of a number added to twice the reciprocal of the square of another number gives 36. The difference of three times the reciprocal of the square of the f

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Question 242912: The reciprocal of the square of a number added to twice the reciprocal of the square of another number gives 36. The difference of three times the reciprocal of the square of the first number and three times the reciprocal of the square of the second number gives -36. What are the numbers?
Can you help me solve this word problem.
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E-2%29%2B%28y%5E-2%29=36%7D=36 (1)
%283x%5E-2%29-%283y%5E-2%29=-36 (2)
Multiply equation (1) by 3 to give %283x%5E-2%29%2B%283y%5E-2%29=108 (3)
Take (2) away from (3) to give %286y%5E-2%29=144%7D%7D+so+%7B%7B%7By+=+sqrt%281%2F24%29
y=0.2041 Or y=-0.2041
So plug y back into our equation (1) gives x to be x+=+%281%2F12%29%5E%281%2F2%29
so x+=+0.2887 or x+=+-0.2887