Question

answer this question hurry..

Answer 1

( x -1/x)² +2( x + 1/x) = 7 1/4 =29/4

(x +1/x)² -4x.1/x + 2( x +1/x) = 29/4

(x + 1/x)² +2( x +1/x) -4 -29/ 4=0

4(x +1/x)² +8(x +1/x) -45 =0

let ( x + 1/x ) = r

4r² +8r -45 =0

4r² +18r -10r -45 =0

2r( 2r +9) -5(2r +9) =0

(2r +9)( 2r -5) =0

r = 5/2 , -9/2

x + 1/x = 5/2

2x² -5x +2 =0

2x² -4x -x +2 =0

2x (x -2)-(x -2) =0

x = 1/2 , 2

and
x + 1/x = -9/2

2x² +9x +2 =0

x = { -9±√81 -16)}/4