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Question Number 137700 by peter frank last updated on 05/Apr/21

Commented by mr W last updated on 05/Apr/21

it′s not true!  example:  b=c=−1, a=(1/( (2)^(1/3) ))  (1/a^3 )+(1/b^3 )+(1/c^3 )=0  but (a+b+c)^3 =((1/( (2)^(1/3) ))−2)^3 ≠27abc=((27)/( (2)^(1/3) ))

$${it}'{s}\:{not}\:{true}! \\ $$$${example}: \\ $$$${b}={c}=−\mathrm{1},\:{a}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{3}} }+\frac{\mathrm{1}}{{b}^{\mathrm{3}} }+\frac{\mathrm{1}}{{c}^{\mathrm{3}} }=\mathrm{0} \\ $$$${but}\:\left({a}+{b}+{c}\right)^{\mathrm{3}} =\left(\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}}−\mathrm{2}\right)^{\mathrm{3}} \neq\mathrm{27}{abc}=\frac{\mathrm{27}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}} \\ $$

Commented by peter frank last updated on 05/Apr/21

thank you so much for confirmation

$${thank}\:{you}\:{so}\:{much}\:{for}\:{confirmation} \\ $$

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