Question

If a = 2 + √3, find the value of (a^2 + 1 /^2 )

Answer 1

Answer:

14

Step-by-step explanation:

Answer 2

Given
———-

a = 2 + Sqrt (3)

Squaring on both sides, we get

a^2 = (2 + Sqrt (3))^2

a^2 = 4 + 3 + 2*2*Sqrt(3)

a^2 = 7 + 4*Sqrt(3) ————> 1

1/a^2 = 1/(7 + 4*Sqrt(3))

Rationalizing

1/a^2 = (7 - 4*Sqrt(3))/((7 + 4*Sqrt(3))*(7 - 4*Sqrt(3))

1/a^2 = (7 - 4*Sqrt(3))/(49 - 48)

1/a^2 = (7 - 4*Sqrt(3)) ———->2

Adding equations 1 & 2,

(a^2 + 1/a^2) = 7 + 4*Sqrt(3) + 7 - 4*Sqrt(3)

(a^2 + 1/a^2) = 14 ——> Answer