Question

If √2+x+√2-x√2+x-√2-x=2, then the value of X is

A) 4⁄5 B) 3⁄5 C) 8/5 D) 1/5

Answer 1

Step-by-step explanation:

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!

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