Question Number 147223 by mathlove last updated on 19/Jul/21 Commented by bramlexs22 last updated on 19/Jul/21 $$\:\:\:\mathrm{2}^{\mathrm{3x}} +\mathrm{2}^{\mathrm{x}} .\mathrm{3}^{\mathrm{2x}} −\mathrm{2}.\mathrm{3}^{\mathrm{3x}} \:=\:\mathrm{0} \\ $$$$\:\begin{cases}{\mathrm{2}^{\mathrm{x}} =\mathrm{u}}\\{\mathrm{3}^{\mathrm{x}} =\mathrm{v}}\end{cases}\:\Rightarrow\mathrm{u}^{\mathrm{3}}…
Question Number 81674 by Power last updated on 14/Feb/20 Commented by Tony Lin last updated on 14/Feb/20 $${let}\:{y}=\mathrm{7}−{x}^{\mathrm{2}} \\ $$$${x}+\left(\mathrm{7}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{11} \\ $$$${x}+\left({x}^{\mathrm{4}} −\mathrm{14}{x}^{\mathrm{2}}…
Question Number 81654 by peter frank last updated on 14/Feb/20 Commented by peter frank last updated on 14/Feb/20 $${we}\:{need}\:{to}\:{prove}\: \\ $$$${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}={a}^{\mathrm{2}} \left({a}^{\mathrm{2}}…
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Question Number 147187 by mathdanisur last updated on 18/Jul/21 $${if}\:\:\left(\overline {{xyz}}\right)^{\mathrm{2}} \:=\:\left({x}+{y}+{z}\right)^{\mathrm{5}} \:\:{then}\:{find}: \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} −\mid\left({x}+{y}+{z}\right)+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\mid \\ $$ Commented by…
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Question Number 81647 by john santu last updated on 14/Feb/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3} \\ $$ Commented by mr W last updated on 14/Feb/20…
Question Number 147183 by mathdanisur last updated on 18/Jul/21 $${prove}\:{that} \\ $$$$\boldsymbol{{e}}^{\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}} \:>\:\frac{\mathrm{13}\:+\:\mathrm{2}\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$ Answered by mindispower last updated on 18/Jul/21 $$\Leftrightarrow{e}^{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}} >\mathrm{1}+\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)\left({E}\right) \\…
Question Number 147169 by mathdanisur last updated on 18/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{5}^{\boldsymbol{{x}}} \:+\:\mathrm{6}^{\boldsymbol{{x}}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\:? \\ $$ Commented by gsk2684 last updated on 18/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}}…