Find a number such that the sum of the number and its reciprocal is 65/8.​

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

b

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