Question

the sum of a number and its reciprocal is 65/8. find the number

Answer 1

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

Answer 2

Let the Number be x,
it's reciprocal is 1/x

x + 1/x = 65/8

x²+1/x=65/8

8x²+8=65x

8x²+8-65x=0

8x²-64x-x+8=0

8x(x-8)-1(x-8)=0

8x-1(x-8)=0

8x - 1 =0

=> 8x=1

=> x=1/8

x-8=0

=> x = 8

Therfore the number is 8 or 1/8