Question

if x is equal to root 5 minus 2 find x square plus 1 by x square

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 !

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Answer 2

Answer :

x = √5 - 2

1 / x = 1 / √5 - 2

1 / x = 1 / √5 - 2 * √5 + 2 / √5 + 2

1 / x = √5 + 2 / 5 - 4

1 / x = √5 + 2

Now,

x + 1 / x = √5 - 2 + √5 + 2

=> 2 √ 5

On squaring both sides,,

x² + 1 / x² + 2 = 20

x² + 1 / x² = 20 - 2

x² + 1 / x² = 18