Question

2(x^2+1/x^2)-(x+1/x)-11=0​

Answer 1

$\huge \sf \bf {\boxed{\underline {\pink{\underline {✠Aɴʂᴡᴇʀ࿐ :−}}}}}$

Hi ,

It is given that b,

2( x² + 1/x² ) - ( x + 1/x ) = 11

2[ ( x + 1/x )² - 2 ] - ( x + 1/x ) - 11 = 0

Let x + 1/x = a ---( 1 )

2 ( a² - 2 ) - a - 11 = 0

2a² - 4 - a - 11 = 0

2a² - a - 15 = 0

2a² - 6a + 5a - 15 = 0

2a( a - 3 ) + 5 ( a - 3 ) = 0

( a - 3 )( 2a + 5 ) = 0

a - 3 = 0 or 2a + 5 = 0

now , from ( 1 ) ,

x + 1/x - 3 = 0 or 2 ( x + 1/x ) + 5 = 0

x² + 1 - 3x = 0 or 2x² + 2 + 5x = 0

x² - 3x + 1 = 0 or 2x² + 5x + 2 = 0

or 2x² + 4x + x + 2 = 0

or 2x( x + 2 ) + ( x + 2 ) = 0

or ( x + 2 ) ( 2x + 1 ) = 0

Therefore ,

x = -2 , x = -1/2 , x² -3x +1 = 0

I hope this helps you.

: )

Answer 2

Step-by-step explanation:

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