Question

If x = 2 + /3, then value of x^2 + 1/x^2 is equal to
______

Answer 1

Answer:

14

Step-by-step explanation:

it is given that x= 2+√3 ,

therefore x² will be equal to (2+√3)²

now expand (2+√3)²

you will get (2+√3)²= 4 +3 +4√3

which can be further simplified to 7+4√3

therefore x² = 7+4√3

now for 1 /x²

put the value of x² in the denominator

you will get 1/(7+4√3)

now rationalise the denominator of this term i.e multiply by it's conjugate

therefore multiply 1/(7+4√3) with (7-4√3)/(7-4√3)

so in the denominator, you can apply the identity (a+b)(a-b)=a²-b²

therefore it will be simplified to

(7-4√3)/(7² - (4√3)²)

now in the denominator 7² =49

and (4√3)² =48

and 49 -48 =1

so 1/x² = 7-4√3

now add x² and 1/x² ,

7+4√3 +7-4√3

you will get 14 as the answer

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