If $x+(4/x)=4$ then $x^3+(4/x)^3$ is

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If $x+(4/x)=4$ then $x^3+(4/x)^3 $is.

Note: $(x+(4/x))^3=4^3$

assuming $4/x=y$ then

$(x+y)^3=64$

$x^3+y^3+3xy^2+3yx^2=64$

$x^3+y^3+3xy(x+y)=64$

$x^3+y^3+3*4(4)=64$

so $x^3+y^3=16$

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1 Answer

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From $x+\frac{4}{x}=4$ we have $x=2$ so that $x^3+(\frac{4}{x})^3=16$

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