Question

(x+(1)/(x))^(2)-2(x-(1)/(x)+4)=11 ​

Answer 1

Answer:

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

2a²-4a-11 = 0

2a²a - 150

2a² - 6a + 5a - 15 = 0

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

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

a 30 or 2a + 5 = 0

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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

Step-by-step explanation:

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