What number subtract it's reciprocal is 1?

Question

	1±25
	-1±52
	2±25
	1±52

Answer 1

You want to solve the equation:

x - 1/x = 1 (note that x cannot equal 0)

x²-1= x (multiply every term by x)

x²-x-1 = 0 (get the quadratic equation in the form ax²+bx+c = 0)

Now use the quadratic formula to get to values for x. These will be irrational numbers.

Once you have solved for the two value of x, check your answers here:

desmos.com/calculator/fosicb40gm

Answer 2

a number, subtract its reciprical equals one

x - 1/x = 1

multiply all 3 terms by x

2 solutions

one positive real, one negative real, by descartes' rule of signs

x^2 -1 = x

x^2 -x -1 = 0

complete the square or use the quadratic formula

x^2 -x + 1/4 = 1 + 1/4 = 5/4

(x-1/2)^2 = 5/4

x-1/2 = +/-sqr(5/4)

x = 1/2 +/- (1/2)sqr5

or

use the quadratic formula

x= 1/2 +/-(1/2)sqr(1+4)

x= 1/2 +/- (1/2)sqr5

or maybe you meant

1/x -x = 1

then

1-x^2 = x

x^2+x =1

x^2 +x + 1/4 = 5/4

(x+1/2)^2 = 5/4

x = -1/2 +/-(1/2)sqr5

still doesn't look like any of the 4 choices

how about

1-1/x = x

x -1 = x^2

x^2-x = -1

(x-1/2)^2 = -1

x = 1/2 +/-i

on a time pressure test I'd probably go with

1st choice: 1+/-25 might mean 1+/-sqr5

or maybe the 3rd: 2+/-25 might mean 2+/-sqr5

closer than 2nd or 4th choices

or

maybe None of the Above was a 5th choice that got cut off