Question

if x=√5+2,then find the value of x²+1/x²​.
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Answer 1

Answer:

the answer is 20because

(2√5) square =20

Answer 2

Hey mate!

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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.

 

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Thanks for the question! ★★★