Question

If a=9+4root 5 and b=1/a then find the value of a^2+b^2

Answer 1

Answer: 161+72(5)^1/2 + 1/(161+72(5)^1/2)

Explanation:

a=9+4(5)^1/2

a^2=

(9+4(5)^1/2)^2=

(9+4(5)^1/2)(9+4(5)^1/2)=

81+9*4(5)^1/2+9*4(5)^1/2+4(5)^1/2 * 4(5)^1/2=

81+36(5)^1/2+36(5)^1/2+16*5=

81+72(5)^1/2+80=161+72(5)^1/2

b^2=

1/a^2=1/(161+72(5)^1/2)

a^2+b^2=161+72(5)^1/2 + 1/(161+72(5)^1/2)