Question

Solve
please as fast as you can ​

Answer 1

Answer:

a + (1 / a) = 5

a ^ 2 + (1 / a ^ 2) = 23

Step-by-step explanation:

Solution,

We have,

a^2 - 5a +1 = 0

a^2 + 1 = 5a

(a^2 + 1) / a = 5

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

a + (1 / a) = 5

Hence, a + (1 / a) = 5

Now,

Again,

a + (1 / a) = 5

Squaring the both sides,

{ a + (1 / a) } ^ 2 = (5) ^ 2

a ^ 2 + 2 . a . (1 / a) + (1 / a) ^ 2 = 25

a ^ 2 + 2 + (1 / a ^ 2) = 25

a ^ 2 + (1 / a ^ 2) = 25 - 2

a ^ 2 + (1 / a ^ 2) =  23

Hence, a ^ 2 + (1 / a ^ 2) = 23