If x = 4-√5, find the value of (x2+1/x2 )

2562 - 960√5/11

Step-by-step explanation:

We are given here the value of x as 4 - √5. We need to find the value of x² + 1/x² . So let's find out 1/x

⇒ x = 4 - √5

⇒ 1/x = 1/4-√5

⇒ 1/x = (4 + √5) / ( 4 - √5) ( 4 + √5 )

⇒ 1/x = 4 + √5 / 4² - (√5)²

⇒ 1/x = 4+√5 / 16 - 5

⇒ 1/x = 4+√5/11

⇒ x² + 1/x² = (4-√5)² + (4+√5)²/11²

⇒ x² + 1/x² = 121( 16 + 5 -8√5 ) + 16 + 5 + 8√5 / 121

⇒ x² + 1/x² = 1936 + 605 - 968√5 + 21 + 8√5 / 121

⇒ x² + 1/x² = 2562 - 960√5/11

answer: 2/4

step-by-step explanation: