Question

$\rm{if \: \: x + \frac{1}{x} = 6 \: \: \: find \: \: {x}^{3} - \frac{1}{ {x}^{3} } }$
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Answer 1

Step-by-step explanation:

x + 1/x = 6

square both side

x^2 + 1/x^2 + 2 = 36

x^2 + 1/x^2 - 2 = 32

(x - 1/x)^2 = 32

x - 1/x = -4root2 , 4root2

cube both sides

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

= -140root2, 140root2