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Question

X2+1/X2=38,X3-1/X3=?

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Solution

x^2 + 1/x^2 = 38
(x - 1/x)^2 + 2 = 38
(x - 1/x)^2 = 38 - 2 = 36
(x - 1/x)^2 = 36
(x - 1/x) = ± 6

left parenthesis x minus 1 over x right parenthesis cubed equals x cubed minus 1 over x cubed minus open square brackets 3 cross times x cross times 1 over x cross times open parentheses x minus 1 over x close parentheses close square brackets 1 right parenthesis space i f space x minus 1 over x space equals space 6 x cubed minus 1 over x cubed equals left parenthesis x minus 1 over x right parenthesis cubed space plus open square brackets 3 cross times x cross times 1 over x cross times open parentheses x minus 1 over x close parentheses close square brackets space space space space space space space space space space space space space space equals space 6 to the power of 3 space end exponent plus space open square brackets 3 cross times 6 close square brackets space equals 216 space plus space 18 space equals 234 1 right parenthesis space i f space x minus 1 over x space equals negative 6 x cubed minus 1 over x cubed equals left parenthesis x minus 1 over x right parenthesis cubed space plus open square brackets 3 cross times x cross times 1 over x cross times open parentheses x minus 1 over x close parentheses close square brackets space space space space space space space space space space space space space space space equals space minus 6 to the power of 3 space end exponent plus space open square brackets 3 cross times negative 6 close square brackets space equals negative 216 space plus thin space minus 18 space space space space space space space space space space space space space space space equals negative 234

so above answer is correct

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