Question

Find the zeroes of the following equation:

1/x = x - 1
What is special about one of the zeroes?

Answer 1

Answer:
`\bold{x=(1\pm \sqrt5)/(2)}`

both zeros are irrational numbers

Explanation:

Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.

`(1)/(x)=x-1\qquad \text{Restriction: }x\\eq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=(-(-1)\pm √((-1)^2-4(1)(-1)))/(2(1))\\\\\\x=(1\pm \sqrt5)/(2)`