Question

Question no. 12..... Help me quick

Answer 1

12)
f(x) = x²-3x+1
a and b are its zeroes
⇒ a²-3a+1 = 0 ⇒ a² +1 = 3a
and b²-3b+1 = 0 ⇒ b² + 1 = 3b


now   a²⁰¹⁴ + b²⁰¹⁴ + a²⁰¹⁶ + b²⁰¹⁶ / a²⁰¹⁵ + b²⁰¹⁵

=  a ²⁰¹⁴ (a²+1) + b²⁰¹⁴(b²+1) / a²⁰¹⁵ + b²⁰¹⁵

a²⁰¹⁴(3a) + b²⁰¹⁴(3b) / a²⁰¹⁵ + b²⁰¹⁵    from above

= 3 (a²⁰¹⁵ + b²⁰¹⁵) / (a²⁰¹⁵ + b²⁰¹⁵)  = 3

hope this helps.