Question

if x2+1/x2=83 find the value of x-1/x

Answer 1

X^2+1/x^2=83

(x-1/x)^2=83-2

x-1/x=9

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

729+3x-1/x=x^3-1/x^3

x^3-1/x^3=729+3 (x-1/x)

=729-27

=702

so your answer is 702

Answer 2

$X^2$+$\frac{1}{x^2}$=83

$(x-\frac{1}{x} )^2$=83-2

$x-\frac{1}{x}$=9

$(x-\frac{1}{x})^{3}$=$x^3$-$3x+\frac{3}{x} -\frac{1}{x^{3} }$

$729+3x$--$\frac{1}{x}$=$x^3$-$\frac{1}{x^{3} }$

$x^3$-$\frac{1}{x^{3} }$ =  $729+3$ $x-\frac{1}{x}$

=$729-27$

=$702$

so ,the answer is 702

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