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Question Number 154372 by mathdanisur last updated on 17/Sep/21 $$\mathrm{If}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{b}\:+\:\mathrm{bc}}\:\geqslant\:\mathrm{1} \\ $$ Terms of Service Privacy…
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Question Number 88811 by jagoll last updated on 13/Apr/20 $$\begin{cases}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({y}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{27}{xy}}\\{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)\:=\mathrm{10}{xy}}\end{cases} \\ $$ Answered by john santu last updated on 13/Apr/20 $${let}\:{me}\:{try}\:…
Question Number 154328 by liberty last updated on 17/Sep/21 $$\:{S}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{10}}+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{10}^{\mathrm{2}} }+\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}^{\mathrm{4}} }+\frac{\mathrm{8}}{\mathrm{1}+\mathrm{10}^{\mathrm{8}} }+\ldots\: \\ $$$$ \\ $$ Answered by MJS_new last updated on 17/Sep/21 $$\mathrm{having}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{we}\:\mathrm{could}\:\mathrm{substract}\:\mathrm{the}…
Question Number 154320 by mathdanisur last updated on 17/Sep/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$ Answered by ghimisi last…
Question Number 154316 by mathdanisur last updated on 17/Sep/21 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\mathrm{y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{xyz}\right)^{\mathrm{2025}} \:-\:\mathrm{1}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 23250 by Tinkutara last updated on 28/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} ,\:{then}\:{prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{{i}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{{j}}{\:^{{n}}…
Question Number 88771 by M±th+et£s last updated on 12/Apr/20 $${solve} \\ $$$${x}^{{x}^{\mathrm{4}} } =\mathrm{64} \\ $$ Commented by mr W last updated on 12/Apr/20 $${x}^{{x}^{\mathrm{4}}…