Answer:
Let the number be x
Since sum of a number and its reciprocal is 65/8 so we have
x+1/x=65/8
8x^2+8=65x
8x^2-65x+8=0
8x^2-64x-x+8=0
8x(x-8)-1(x-8)=0
(8x-1)(x-8)=0
x=8,1/8
So the numbers are 8 or 1/8
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