Question

2(x^2+1/x^2)-(x+1/x)=1
Equation reducible to quadratic form

Answer 1

Answer:

Hey mate here is your answer.

✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡✡

Step-by-step explanation:

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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.

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I hope this helps you.✔✔✔

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