Question

If x = (2 - √5), then x² + 1/x² = ......

Answer 1

Answer:

18

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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Answer 2

Answer:

x²+1/x²=-2

Step-by-step explanation:

x=2-√5

we know that [x+1/x]²=x²+1/x²+2*x*1/x

[x+1/x]²-2=x²+1/x²

here value of x is 2-√5 and 1/x is 1/2-√5

by rationalizing the denominator we get 1/x as -2+√5

now putting the values

2-√5-2+√5-2=x²+1/x²

-2=x²+1/x²

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