Question

If x = 3−√132, what is the value of x2+ 1/x2

Answer 1

Given :   x =( 3−√13 )/2

To Find :   the value of x²+ 1/x²

Solution:

x = ( 3−√13 )/2

1/x   = 2/ ( 3−√13 )

on rationalizing

1/x  =  2(3 + √13)/(9 - 13)

1/x  =  - (3 + √13)/2

x  + 1/x    =  ( 3 −√13 )/2   -  (3 + √13)/2

=> x + 1/x  =    -√13

Squaring both sides

=> x²  + 1/x²  + 2x(1/x)= 13

=>x²  + 1/x²  + 2 = 13

=> x²  + 1/x²  = 11

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Answer 2

Answer:

x = (3-√13)/2

1 / x = 2 / (3 - √13)

on rationalizing

1/x = 2(3+√13)/(9-13)

1/x = - (3+√13)/2

x + 1/x = (3-√13 )/2 (3+√13)/2

=> x + 1/x = -√13

Squaring both sides

=> x² + 1/x² + 2x(1/x)= 13

=>x² +1/x² + 2 = 13

=> x² +1/x² = 11.