Question

x=sqrt(5)-2` Find ` x^(3)+(1)/(x^(3))​

Answer 1

Answer:

Given :

x = √5 + 2

To find :

x² + 1 / x²

Solution :

x = √5 + 2

⇒ 1 / x = 1 / √5 + 2

⇒ 1 / x = 1 / √5 + 2 ×  √5 - 2 /  √5 - 2

⇒ 1 / x =  √5 - 2 / ( √5 )² - ( 2 ) ²

⇒ 1 / x =  √5 - 2 / 5 - 4

⇒ 1 / x =  √5 - 2

Now,

x + 1 / x =  √5 + 2 +  √5 - 2

x + 1 / x = 2 √5

Again,

On squaring both sides, we have ;

( x + 1 / x )² = ( 2 √5 ) ²

⇒ x² + 1 / x² + 2 = 20

⇒ x² + 1 / x² = 20 - 2

⇒ x² + 1 / x² = 18