Question

If
the value of
x = 2-√3, then
find
the
value of x²+1/x²

​

Answer 1

Answer:

the answer is above

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Answer 2

Answer:

x^2 + 1/x^2 = 14  

Step-by-step explanation:

x^2 + 1/ x^2

= ( 2-√3)^ 2  +  1/ ( 2-√3)^2

using the formula : (a-b)^2 = a^2 +b^2 - 2ab

(2-√3)^2 = 4 + 3 - 2 ×  2 ×  √3

          x^2    = 7 - 4√3 .

hence :

( 7 -  4√3 ) + 1/ ( 7- 4√3 )

now we have to rationalize 1/ ( 7 - 4√3)

so we have to multiply ( 7 + 4√3 ) to the numerator and denominator

=1 × ( 7 + 4√3 ) / ( 7 - 4√3 ) × ( 7 + 4√3 )

=( 7 + 4√3 ) / ( 7 ) ^2 - ( 4√3 )^2

= ( 7 + 4√3) / 49 - 16 × √3 × √3

= ( 7 + 4√3) / 49 - 16 × 3

= ( 7 + 4√3) / 49 - 48

1 / x^2 = ( 7 + 4√3) .

x^2 + 1 / x^2 = ( 7 - 4√3 ) + ( 7 + 4√3 )

       open brackets

= 7 - 4√3 + 7 + 4√3                                       ( underlined = cancelled )

= 7 + 7

= 14

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