Easy Number – Give it

[Robert]

Give the positive number which is equal to its inverse plus one?

[scott]

The number is 8/5 . Is my finding right.
I got it as follows:
Let the number be x. Then given
x=(1/x)+1 solving this we get x=8/5

[jamesravid]

Scott,

I think your answer is wrong.

let me prove this...

if x=8/5 then

=> 8/5 = 5/8 +1
=> 8/5 = 13/8
=> 8 *8/5 *13 =1
=> 64/65 =1

which is wrong...

I believe the x is a complex number if x^2 -x -1 =0

-- James.

[scott]

James I think you have made a small mistake.
The 8/5=5/8+1 gives
8/5=13/8 which means
(8/5)* (8/13) = 1 and this true because you get .98 which is equal to 1
and not as you said 8 *8/5 *13 =1
Also the equation for solving is x^2 -x+1 =0 and not as you mentioned x^2 -x -1 =0

Hope my explanation is correct.

[jamesravid]

Scott,

let me explain the equation part first,

it is given that x = 1/x +1
=> x = (1+x)/x
=> x^2 = 1+x
=> x^2 -x-1 =0

if 0.98 is equal to 1 then you answer is right


-- James.