Question

the value of x for which 9(x²+1/x²)-27(x+1/x)​

Answer 1

Answer:

Step-by-step explanation:

given equation is 9(x^2 + 1/x^2) - 27(x + 1/x) + 8 = 0

let x + 1/x = t

9(t^2 - 2) - 27t + 8 = 0

9t^2 - 27t - 10 =0

(3t - 10)(3t + 1) = 0

t = 10/3 , -1/3

t = 10/3

x + 1/x = 10/3  

3x^2 - 10x + 3 = 0

(3x - 1)(x - 3) = 0

x = 3 , 1/3  

t = -1/3

x + 1/x = -1/3

3x^2 + x + 3 = 0-------(1)

D = b^2 - 4ac

  = 1 - 36

  = -35                 (negative)

equation (1) is always positive ,hence no root  

root of the given equation is  x = 3, 1/3

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