Question

if x = 2+√3 find x²+1/x²​

Answer 1

EXPLANATION.

⇒ x = 2 + √3.

As we know that,

⇒ 1/x = 1/2 + √3.

Rationalize the equation, we get.

⇒ 1/x = 1/2 + √3 x (2 - √3)/(2 - √3).

⇒ 1/x = (2 - √3)/(2 + √3)(2 - √3).

⇒ 1/x = (2 - √3)/[(2)² - (√3)²].

⇒ 1/x = (2 - √3)/(4 - 3).

⇒ 1/x = 2 - √3.

To find :

⇒ x² + 1/x².

⇒ (2 + √3)² + (2 - √3)².

⇒ 4 + 3 + 4√3 + 4 + 3 - 4√3.

⇒ 7 + 7 = 14.

⇒ x² + 1/x² = 14.

Answer 2

Step-by-step explanation:

if x=2+√3

find = x^2 +1/x^2

then put x value in x^2 +1/x^2

(2+√3)^2 + 1/(2+√3)^2

here,a=2 and b=√3

so the formula is a^2 +b^2 +2ab

2^2 +(√3)^2 +(2×2×√3)

4+3+4√3

7+4√3

so this value put in x value

7+4√3 + 1/7+4√3

13.9+1/13.9

(193.6+1)/13.9

194.6/13.9

14