Question

If x = 7+ 4root3, find x +1/x​

Answer 1

Explanation:

please refer to the attachment

Answer 2

Answer:

Hence, the value of x + 1/x is 14.

Explanation:

Given:-

x = 7 + 4√3

To find out:-

Value of x + 1/x

Solution:-

We have

x = 7 + 4√3

∴ 1/x = 1/(7 + 4√3)

The denomination = 7 + 4√3

We know that

Rationalising factor of a + b√c = a - b√c.

So, rationalising factor of 7 + 4√3 = 7 - 4√3.

On rationalising the denominator them

1/x = [1/(7 + 4√3)] × [(7 - 4√3)/(7 - 4√3)]

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

Now, applying algebraic Identity in denominator because it is in the form of:

(a + b)(a + b) = a ^2 - b^2

Where, we have to put in our expression a = 7 and b = 4√3, We get

1/x = (7 - 4√3)/[(7)^2 - (4√3)^2]

1/x = (7 - 4√3)/(49 - 48)

1/x = (7 - 4√3)/1

1/x = 7 - 4√3

Now, adding both values x and 1/x , we get

→ x + 1/x = (7 + 4√3)+(7 - 4√3)

[Open brackets]

→ x + 1/x = 7 + 4√3 + 7 - 4√3

[4√3 will cancel out]

→ x + 1/x = 7 + 7

→ x + 1/x = 14

Answer:-

Hence, the value of x + 1/x is 14.

Used formula:-

Rationalising factor of a + b√c = a - b√c.

(a + b)(a + b) = a ^2 - b^2