Question

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

Hey mate!(●ˇ∀ˇ●)

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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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Answer 2

Answer:

x=√5+2

x^2=(√5+2)^2

=(√5)^2+2.√5.2+(2)^2

=5+4√5+4

=9+4√5

1/x^2

=1/(9+4√5)^2

=(9-4√5)/(9+4√5)(9-4√5)

=(9-4√5)/{(9)^2-(4√5)^2}

=(9-4√5)/(81-80)

=(9-4√5)

x^2+1/x^2

=9+4√5+9-4√5

=18