Question Number 169445 by infinityaction last updated on 30/Apr/22
$$ \\ $$$$\:\:\:\mathrm{let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} \:+\mathrm{30xy}\:=\:\mathrm{2000} \\ $$$$\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{10} \\ $$
Commented by mr W last updated on 30/Apr/22
$${i}\:{don}'{t}\:{think}\:{one}\:{can}\:{show}\:{this}, \\ $$$${because}\:{it}'{s}\:{not}\:{true}. \\ $$
Commented by infinityaction last updated on 30/Apr/22
$${how}\:{sir} \\ $$
Commented by infinityaction last updated on 30/Apr/22
Commented by infinityaction last updated on 30/Apr/22
$${sorry}\:{sir}\:{my}\:{mistake} \\ $$$${not}\:\left({x}+{y}\right)\:{replace}\:\left({x}+{y}\right)^{\mathrm{3}} \\ $$
Commented by mr W last updated on 30/Apr/22
$${it}'{s}\:{still}\:{not}\:{true}! \\ $$$${try}\:{with}\:\mathrm{10}\left({x}+{y}\right)^{\mathrm{2}} . \\ $$
Commented by infinityaction last updated on 30/Apr/22
$${sir}\:{today}\:{i}\:{am}\:{ill}\:{due}\:{to}\:{which}\:{these}\:{are}\: \\ $$$${mistakes}\:{happened}\:{i}\:{am}\:{sorry} \\ $$
Commented by mr W last updated on 30/Apr/22
$${get}\:{well}\:{soon}! \\ $$$${i}\:{think}\:{there}\:{are}\:{two}\:{possibilities}: \\ $$$${replace}\:\mathrm{10}\left({x}+{y}\right)\:{with}\:\mathrm{10}\left({x}+{y}\right)^{\mathrm{2}} \:{or} \\ $$$${replace}\:\mathrm{10}\left({x}+{y}\right)\:{with}\:\left({x}+{y}\right)^{\mathrm{3}} . \\ $$
Commented by infinityaction last updated on 01/May/22
$${oh}\:{yes} \\ $$$$\:\:{thanks}\:{you}\:{sir} \\ $$