I have been working on this question all day and can not figure out what to do.

The question says according to the Quadratic Formula, the solutions of x^2-x-1=0
I know the positive solution is the golden rule ratio and the negative solution is the conjugate of 0(with a slash through it) and is denoted with a 0with a slash and phi bar above it.

I just cannot figure out how to use a calculator to write the decimal expansions of 0 (with a slash through it) and 0 with a slash and phi bar above it rounded to six decimal places (to the right of the decimal point. Describe the relationship between the decimal expansions.

I am not understanding this problem at all. The notes I have are not any help either.
Thanks for any help

x= (1+-sqrt(5))/2=

1+sqrt 5/ 2 = = 1.61803399
(1-sqrt 5)/2= -1.23606798

relationship? multiplied, they equal -2

Hint. Use your google search window as a calculator

To find the decimal expansions of the solutions to the equation x^2-x-1=0 using a calculator, we need to use the Quadratic Formula. The Quadratic Formula states that for any quadratic equation of the form ax^2+bx+c=0, the solutions for x can be found using the formula:

x = (-b ± √(b^2-4ac))/(2a)

In your case, the equation x^2-x-1=0 is written in the form ax^2+bx+c=0, where a=1, b=-1, and c=-1. Plugging these values into the quadratic formula, we have:

x = (-(-1) ± √((-1)^2-4(1)(-1)))/(2(1))

Simplifying further, we get:

x = (1 ± √(1+4))/2

To evaluate the square root (√) using a calculator, you need to input the number inside the square root and press the square root symbol (√) or the radical button.

Now, let's find the decimal expansions of the solutions. Evaluating the expression, we have:

x = (1 ± √5)/2

The positive solution is obtained by using the plus sign, so we have:

x = (1 + √5)/2

The negative solution is obtained by using the minus sign, so we have:

x = (1 - √5)/2

To write these decimal expansions rounded to six decimal places, you can use a calculator that has the capability to display the desired accuracy. Enter (1 + √5)/2 into your calculator and press the equals (=) button. Take note of the decimal expansion up to six decimal places. Then enter (1 - √5)/2 and again, note the decimal expansion up to six decimal places.

The relationship between the decimal expansions of (1 + √5)/2 and (1 - √5)/2 is that they are additive inverses of each other. In other words, their decimal expansions are the same, except one is positive while the other is negative. This is because the quadratic equation x^2-x-1=0 has two solutions, one positive and one negative, and they are the exact opposites of each other.

I hope this helps you understand how to use a calculator to find the decimal expansions of the solutions to the given quadratic equation and the relationship between those solutions.