X+1/x=7
=(x^2+1)/x=7
=x^2+1=7x
=x^2=7x-1

x^4-1/x^4
={(x^2)^2}-1/{(x^2)^2}
={(7x-1)^2}-1/{(7x-1)^2}
={49x-14x+1)}-1/{49x-14x+1}
={35x+1}-1/{35x+1}
=[{(35x+1)^2}-1]/(35x+1)
=35x • (35x + 2) /(35x + 1)

Problem:
If x * (1/x) = 7, find the value of x^4 - 1/x^4.

Solution:

Step 1: Identify the given equation
The given equation is x * (1/x) = 7.

Step 2: Simplify the equation
Multiplying x with (1/x) gives us 1, so the equation simplifies to 1 = 7.

Step 3: Evaluate the equation
The equation 1 = 7 is not possible as it contradicts basic mathematics. Therefore, there is no solution for the given equation x * (1/x) = 7.

Explanation:
The given equation x * (1/x) = 7 is not possible as it leads to a contradiction. This means that there is no value of x that satisfies the equation. Therefore, it is not possible to find the value of x^4 - 1/x^4.

The equation x * (1/x) = 7 can be simplified as x^2 = 7. However, even in this simplified form, there is no solution. This is because the square of any real number cannot be equal to 7.

In mathematics, we use the concept of inverse functions to solve equations like x * (1/x) = 7. The inverse of multiplication is division, so we can rewrite the equation as x / x = 7. This simplifies to 1 = 7, which is a contradiction.

Therefore, the given equation has no solution, and consequently, it is not possible to find the value of x^4 - 1/x^4.

Conclusion:
The equation x * (1/x) = 7 does not have a solution. As a result, it is not possible to find the value of x^4 - 1/x^4.