Question

if x=2+√3 then what is the value of x²+1/x² please send with procedure.. correct answer will be marked brainliest..

Answer 1

Answer :

x² + 1/x² = 14

Solution :

• Given : x = 2 + √3
• To find : x² + 1/x² = ?

We have ;

x = 2 + √3

Thus ,

1/x = 1/(2 + √3)

Now ,

Rationalising the denominator of the term in RHS , we have ;

=> 1/x = (2 - √3) / (2 + √3)(2 - √3)

=> 1/x = (2 - √3) / [ 2² - (√3)² ]

=> 1/x = (2 - √3) / (4 - 3)

=> 1/x = (2 - √3) / 1

=> 1/x = 2 - √3

Now ,

=> x + 1/x = 2 + √3 + 2 - √3

=> x + 1/x = 4

Now ,

Squaring both the sides , we have ;

=> (x + 1/x)² = 4²

=> x² + (1/x)² + 2•x•(1/x).= 16

=> x² + 1/x² + 2 = 16

=> x² + 1/x² = 16 - 2

=> x² + 1/x² = 14

Hence , x² + 1/x² = 14 .

Answer 2

Step-by-step explanation:

14 is the answer...

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