If x=2+√3, Find the value of x^2+1/x^2

1.	If x=2+√3, Find the value of x^2+1/x^2
Answer» Given thatx = 2 + √31/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√31/x^2 = (2 - √3)^2= (2)^2 + (√3)^2 - 2 × 2 × √3= 4 + 3 - 4√3= 7 - 4√3x^2 + 1/x^2= (7 + 4√3) + (7 - 4√3)= 7 + 4√3 + 7 - 4√3= 7 + 7 + 4√3 - 4√3= 14

Discussion