**Solution:**

To find the value of **x^4 1/x^4**, we can simplify the expression step by step.

**Step 1:**
First, let's solve the quadratic equation **x^2 - x - 1 = 0** using the quadratic formula:

The quadratic formula is given by **x = (-b ± √(b^2 - 4ac))/(2a)**, where a, b, and c are the coefficients of the quadratic equation.

For the given equation **x^2 - x - 1 = 0**, we have:
a = 1, b = -1, and c = -1.

Using the quadratic formula, we can find the values of x:

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

Simplifying the equation further:
**x = (1 ± √(1 + 4))/2**

**x = (1 ± √5)/2**

Therefore, the solutions to the quadratic equation are:
**x = (1 + √5)/2** and **x = (1 - √5)/2**

**Step 2:**
Now, let's calculate the value of **x^4 1/x^4** using the solutions obtained in Step 1.

Let's consider the first solution **x = (1 + √5)/2**:

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

Simplifying the expression further:
**x^4 1/x^4 = (1 + √5)^4 / (1 + √5)^4**

Since the numerator and denominator are the same, the expression simplifies to:
**x^4 1/x^4 = 1**

Similarly, for the second solution **x = (1 - √5)/2**, we can follow the same steps and find that:
**x^4 1/x^4 = 1**

Therefore, for both solutions of the quadratic equation **x^2 - x - 1 = 0**, the value of **x^4 1/x^4** is equal to 1.

In summary:
- The solutions to the quadratic equation **x^2 - x - 1 = 0** are **x = (1 + √5)/2** and **x = (1 - √5)/2**.
- For both solutions, the value of **x^4 1/x^4** is equal to 1.

In the equation we suppose that x^4=tthen we see x^4 = t = x^2 - 2x +1 by squarin the given equationnow we can arrange this x^4 = (x^2 +x-1) -3x+2thus x^4 = 0 -3x+2put this value in the equation of x^4+1/x^4we can get a equation like (9x^2-12x+4+1)/2-3xthen arrange the answer like (9(x^2+x-1)-21x+14)/2-3xas we see that -21x+14/2-3xso by this we can get 7 which is the right answer