Question

solve for x..........​

Answer 1

x^2 + 1/x^2 = ( x+1/x)^2 - 2

So

2( (x+1/x)^2 - 2)) - 9( x+1/x) +14= 0

2( x+1/x)^2 - 4 - 9( x+1/x) +14 = 0

2( x+1/x)^2 - 9( x+ 1/x) + 10 = 0

2(x+1/x)^2 - 4( x+1/x) - 5( x+1/x) +10= 0

2(x+1/x)( ( x+1/x) - 2)) - 5( x+1/x - 2) = 0

( 2( x+1/x) - 5) ( x+1/x. -2) = 0

2( x+1/x) - 5 = 0

2( x+1/x) = 5

x+ 1/x = 5/2

Its obvious that x= 2

as 2 +1/2 = 5/2

x^2 + 1 - 5/2 x = 0

2x^2 - 5x + 2 = 0

2x^2 -4x -x +2 = 0

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

2x-1 = 0, x-2= 0

x= 1/2, 2

ALSo

x+1/x -2 = 0

x+1/x = 2

its obvious its x= 1

x^2 + 1 - 2x = 0

( x-1)^2 = 0

x= 1

So x= 1, 1/2, 2

So its (A) option