Question

If,a+1/a=2,Find: a⁴+1/a⁴

Answer 1

Answer:

Step-by-step explanation:

a + 1/a = 2

(a + 1/a)² = 2²                    squaring on both side

a² + 1/a² + 2*a*1/a = 4

a² + 1/a²  = 4 - 2

a² + 1/a²  = 2 --- -- (i)

Now

from (i)

(a² + 1/a²)²  = 2²                 squaring on both side

a⁴ + 1/a⁴ + 2*a²*1/a² = 4

a⁴ + 1/a⁴  = 4 - 2

a⁴ + 1/a⁴  = 2