Given:
x = 7 - 4√3

To Find:
The value of x * 1/x

Solution:

Let's simplify the expression step by step.

Step 1:
To find the value of x * 1/x, we need to find the value of x and 1/x separately.

Step 2:
We are given that x = 7 - 4√3.

Step 3:
To find the value of x, substitute the given expression into x.

x = 7 - 4√3

Step 4:
We can simplify this expression further by rationalizing the denominator.

x = 7 - 4√3
= 7 - 4√3 * √3/√3
= 7 - 4 * √9/√3
= 7 - 4 * 3/√3
= 7 - 12/√3
= 7 - 12√3/3
= 7 - 4√3

Step 5:
Now, let's find the value of 1/x.

1/x = 1/(7 - 4√3)

Step 6:
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator.

1/x = (1 * (7 + 4√3))/((7 - 4√3) * (7 + 4√3))

Step 7:
Simplifying further,

1/x = (7 + 4√3)/(49 - 16 * 3)
= (7 + 4√3)/(49 - 48)
= (7 + 4√3)/1
= 7 + 4√3

Step 8:
Now, let's find the value of x * 1/x.

x * 1/x = (7 - 4√3) * (7 + 4√3)

Step 9:
Using the difference of squares formula, (a + b)(a - b) = a^2 - b^2, we simplify further.

x * 1/x = 7^2 - (4√3)^2
= 49 - 16 * 3
= 49 - 48
= 1

Conclusion:
The value of x * 1/x is 1.

X = 7-4√3 then, 1/x = 1/ 7-4√3 = 1/ 7-4√3 × 7+4√3 /7+4√3 = 7+4√3 / (7)² - (4√3)² = 7+4√3 / 49 -48 = 7+4√3 /1 = 7+4√3 then we find the value of x +1/x = 7-4√3 +7+4√3 = 14