Question

5) If x=2+√3 find
²+1/x²
​

Answer 1

Answer:

14

Step-by-step explanation:

given x=2+√3

so,1/x=2-√3

x2=(2+√3)²=4+3+4√3=7+4√3

1/x²=(2-√3)²= 4+3-4√3=7-4√3

therefore,x2+1/x2=7+4√3+7-4√3=14

Answer 2

Given that
x = 2 + √3
1/x = 1/2 + √3
= 1 × (2 - √3)/(2 + √3) (2 - √3)
= (2 - √3)/(2^2 - √3^2)
= (2 - √3)/4 - 3
= (2 - √3)
Therefore ,
x^2 = (2 + √3)
= (2)^2 + (√3)^2 + 2 × 2 × √3
= 4 + 3 + 4√3
= 7 + 4√3
1/x^2 = (2 - √3)^2
= (2)^2 + (√3)^2 - 2 × 2 × √3
= 4 + 3 - 4√3
= 7 - 4√3
x^2 + 1/x^2
= (7 + 4√3) + (7 - 4√3)
= 7 + 4√3 + 7 - 4√3
= 7 + 7 + 4√3 - 4√3
= 14