Question

If a^2-4a+1=0, the find out a^3+1/a^3

Answer 1

Answer :

Pls refer to the attachment above to get your required solution to this question.
Basically, in this type of questions , somehow by using the given equation, we have to find the value of a +1/a.
Then we can find anything with the help of it.

Answer 2

Answer :

52

Step-by-step explanation :

a² - 4a + 1 = 0

a² - 4a = -1

a ( a - 4 ) = - 1

( a - 4 ) = - 1 / a

a + 1 / a = 4

Now, on cubing both sides ;

( a + 1 / a )³  = ( 4 )³

⇒ a³ + 1 / a³ + 3 ( a + 1 / a ) = 64

⇒ a³ + 1 / a³ + 3 * 4 = 64

⇒ a³ + 1 / a³ + 12 = 64

⇒ a³ + 1 / a³ = 64 - 12

⇒ a³ + 1 / a³ = 52

Hence, the answer is 52.