Question

if x = √ 5 - 2 find x2 + 1/x2

Answer 1

Hey mate!

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Given :

x = √5 - 2

To find :

1) x + 1 / x

2) 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

And, on squaring both sides,

( x + 1/x )² = (2√5) ²

⇒ x² + 1 / x² + 2 = 20

⇒ x² + 1 / x² = 20 - 2

⇒ x² + 1 / x² = 18.

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Thanks for the question !

☺️☺️☺️

Answer 2

Hello Dude!

______________________

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

on squaring both sides,

( x + 1/x )² = (2√5) ²

=> x² + 1 / x² + 2 = 20

=> x² + 1 / x² = 20 - 2

=> x² + 1 / x² = 18.

_______________________

Thanks for the question !

@Aaisha44 ❤️