Question

if a² - 3a -1 = 0 then find a² + 1/a²​

Answer 1

a² - 3a -1= 0

a² - 1 = 3a

(a² - 1)/a = 3a/a. {dividing the equation by a}

a - 1/a = 3

a² + 1/a² - 2 = (a-1/a)²

a² + 1/a² - 2 = (3)²

a² + 1/a² - 2 = 9

a² + 1/a² = 11

Answer 2

Step-by-step explanation:

a² - 3a - 1 = 0

=> a² - 1 = 3a

From the given equation divide by a from both side.

a² - 1 = 3a

=> (a² - 1 ) / a = 3a / a

=> a - 1/a = 3

We know,

( a - 1/a)² = a² + 1/a² - 2 { where a ≠ 0}

=> (a - 1/a)² + 2 = a² + 1/a²

=> 3² + 2 = a² + 1/a² { since, (a - 1/a)² = 3) }

=> 9 + 2 = a² + 1/a²

=> 11 = a² + 1/a²

Hope it will help