Question

if x =(2+root3)find the value of x square+1/xsquar

Answer 1

se the solution in the attachment

Answer 2

Hence, the value of x^2 + 1/x^2 is 14.

Step-by-step explanation:

Given:-

x = 2 + √3

To find out:-

Value of x^2 + 1 / x^2

Solution:-

We have,

x = 2 + √3

∴ 1/x = 1/2+√3

The denomination = 2+√3

We know that

Rationalising factor of a+√b = a-√b

So, the rationalising factor of 2+√3 = 2-√3

On rationalising the denominator then

1/x = [1/(2+√3)]×[(2-√3)/2-√3)]

1/x = [1(2-√3)]/[(2+√3)(2-√3)]

1/x = (2-√3)/[(2+√3)(2-√3)]

Now, we will apply algebraic Identity in denominator because the denominator is in the form of

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

Where we have to put a = 2 and b = √3

1/x = (2-√3)/[(2)^2 - (√3)^2]

1/x = (2-√3)/(4 - 3)

1/x = (2-√3)/1

1/x = 2-√3

Now, we have to add both values x and 1/x, we get

∴ x + 1/x = 2+√3+2-√3

√3 will be cancel because they are in unlick singn , so we will cancel them.

x + 1/x = 2 + 2

x + 1/x = 4

Now, squaring on both, we get

(x +1/x)^2 = (4)^2

Using algebraic Identity,

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

Where we have to put a = x and b = 1/x , we get

➟ x^2 + 2(x)(1/x) + (1/x)^2 = 16

➟ x^2 + 2 + (1/x)^2 = 16

➟ x^2 + 2 + 1/x^2 = 16

➟ x^2 + 1/x^2 = 16 - 2

➟ x^2 + 1/x^2 = 14

Answer:-

Hence, the value of x^2 + 1/x^2 is 14.

Used formulae:-

Rationalising factor of a+√b = a-√b

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

(a+b)^2 = a^2 + 2ab + b^2.

I hope it's help you. ☺️