SOLUTION: Find two numbers such that their difference is equal to their product and the sum of their reciprocal a is 5.

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Question 909098: Find two numbers such that their difference is equal to their product and the sum of their reciprocal a is 5.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

two numbers, x and y, such that their difference,x-y is equal to their product x%2Ay
so,x-y=xy...eq.1
and the sum of their reciprocal,1%2Fx and 1%2Fy, is 5.
so, 1%2Fx%2B1%2Fy=5 ....eq.2
start with x-y=xy...eq.1 and solve for x
x-xy=y
x%281-y%29=y
x=+y%2F%281-y%29+
plug it in eq.2

1%2Fx%2B1%2Fy=5 ....eq.2
1%2F%28y%2F%281-y%29%29%2B1%2Fy=5 ...solve for y
%281-y%29%2Fy%2B1%2Fy=5
%28%281-y%29%2B1%29%2Fy=5
%282-y%29%2Fy=5
2-y=5y
2=5y%2By
2=6y
2%2F6=y
highlight%28y=1%2F3%29
now find x

x=+y%2F%281-y%29+
x=+%281%2F3%29%2F%281-1%2F3%29+
x=+%281%2F3%29%2F%282%2F3%29+
x=+%281%2A3%29%2F%283%2A2%29+
x=+%281%2Across%283%29%29%2F%28cross%283%29%2A2%29+
highlight%28x=+1%2F2%29+
check:
x-y=xy...eq.1
1%2F2-1%2F3=%281%2F2%29%2A%281%2F3%29
1%2A3%2F2%2A3-1%2A2%2F3%2A2=1%2F6
3%2F6-2%2F6=1%2F6
%283-2%29%2F6=1%2F6
1%2F6=1%2F6 ...