Given:
X^2 + 1/X^2 = 7

To find:
(X^3)/(X^3)

Solution:

We are given the equation X^2 + 1/X^2 = 7. We need to find the value of (X^3)/(X^3). Let's solve this step by step.

Step 1: Rewrite the equation
We can rewrite the given equation as (X^2 * X^2 + 1)/(X^2) = 7.

Step 2: Simplify the equation
Expanding the numerator, we get (X^4 + 1)/(X^2) = 7.

Step 3: Cross-multiply
Multiplying both sides of the equation by X^2, we get X^4 + 1 = 7X^2.

Step 4: Rearrange the equation
Rearranging the equation, we have X^4 - 7X^2 + 1 = 0.

Step 5: Solve the equation
To find the value of X, we can use either factoring or the quadratic formula. However, the given equation is a quartic equation, and solving quartic equations can be complex. In this case, we will use numerical methods or a graphing calculator.

Step 6: Substitute the value of X
Once we find the value of X, we can substitute it into the expression (X^3)/(X^3) to find the desired value.

Step 7: Calculate the value
Finally, calculate (X^3)/(X^3) using the value of X obtained in the previous step.

Note: Without the specific value of X, we cannot determine the value of (X^3)/(X^3). The solution to the given equation can provide the value of X, and then we can find the value of (X^3)/(X^3) by substituting it.

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