Question

If x = 2+root 3. Find the value of [x²+ 1/x²]​

Answer 1

Answer:

14

Step-by-step explanation:

x=2+√3

x²+ 1/x²=

x²=(2+√3)²

   =4+3+4√3

   =7+4√3

x²+ 1/x²=7+4√3+1/7+4√3

             (7+4√3)²+1/7+4√3

             7²+(4√3)²+56√3+1/7+4√3

             49+48+56√3+1/7+4√3

             98+56√3/7+4√3

             14(7+4√3)/7+4√3

             14

Answer 2

Step-by-step explanation:

Question:-

If x = 2 + √3, find the value of x² + 1/x²

To find:-

The value of x² + 1/x² = ?

Solution:-

Let's solve the problem

We have: x = 2+√3

∴ 1/x = 1/2+√3

The denominator is 2+√3. Multiplying the numerator and denomination by 2-√3, we get

➟ 1/2+√3 × 2-√3/2-√3

➟ 1(2-√3)/(2+√3)(2-√3)

⬤ Applying Algebraic Identity

(a+b)(a-b) = a² - b² to the denominator

We get,

➟ 2-√3 /(2)² - (√3)²

➟ 2 - √3 / 4 - 3

➟ 2 - √3 / 1

➟ 2 -√3

∴ x + 1/x = 2+√3 + 2-√3

x + 1/x = 2 + 2

x + 1/x = 4

Squaring on both sides we get,

(x + 1/x)² = (4)²

➟ x² + 2(x)(1/x) + (1/x)² = 16

➟ x² + 2 + 1/x² = 16

➟ x² + 1/x² = 16 - 2

➟ x² + 1/x² = 14

Answer:-

Hence, the value of x² + 1/x² = 14.

Used Formulae:-

• (a+b)(a-b) = a² - b²

:)