Question

2) If x = √5 +2 find the value the Value fox +
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Answer 1

Answer:

Brainly.in

gayathrisakthivel328

27.10.2018

Math

Secondary School

answered • expert verified

If x = √5+2 find the value of x2 + 1/x2

2

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BrainlyQueen01

BrainlyQueen01

Hey mate!

_______________________

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

Hence,

The value of x² + 1 / x² = 18.

Step-by-step explanation:

l hope it will helpful for u