Question Number 60980 by Tawa1 last updated on 28/May/19 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z} \\ $$$$\:\:\:\:\:\mathrm{x}\left(\mathrm{y}\:+\:\mathrm{z}\right)\:=\:\mathrm{33}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\mathrm{y}\left(\mathrm{z}\:+\:\mathrm{x}\right)\:=\:\mathrm{35}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\mathrm{z}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:\mathrm{14}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{iii}\right) \\ $$ Commented by Prithwish sen last updated on…
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Question Number 192039 by universe last updated on 06/May/23 $$\mathrm{let}\:{x},{y},{z}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} \:=\:\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of} \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }\:+\:\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }\:+\:\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} }…
Question Number 126484 by Mathgreat last updated on 20/Dec/20 Commented by MJS_new last updated on 20/Dec/20 $$\approx\mathrm{1}.\mathrm{63507847} \\ $$ Commented by Mathgreat last updated on…
Question Number 60946 by Tawa1 last updated on 27/May/19 $$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{2x} \\ $$ Commented by Prithwish sen last updated on 27/May/19 $$\mathrm{x}=\mathrm{2} \\ $$ Commented…
Question Number 126482 by ayyoubmaths last updated on 20/Dec/20 Answered by Dwaipayan Shikari last updated on 20/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{cosx}−\mathrm{1}}{{x}}\right)=−\frac{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{{x}}=−\frac{{x}^{\mathrm{2}} }{\mathrm{2}{x}}=\mathrm{0} \\ $$ Terms of…
Question Number 192009 by universe last updated on 05/May/23 $$\:\:\:\:\:{if}\:\:{a}>\mathrm{1}\:,\:{show} \\ $$$$\:\:\:\:\:\frac{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}+\sqrt{{k}}}}{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}−\sqrt{{k}}}}\:\:\:=\:\:\:\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1} \\ $$ Answered by Skabetix last updated…
Question Number 60910 by Tawa1 last updated on 27/May/19 Commented by Rasheed.Sindhi last updated on 27/May/19 $${S}\mathrm{olve}\:\mathrm{the}\:\mathrm{equation}\:\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:−\:\mathrm{4x}\left(\mathrm{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:\:=\:\:\:\mathrm{0} \\ $$$$ \\ $$$${x}^{\mathrm{4}} +{x}^{\mathrm{2}}…
Question Number 60905 by necx1 last updated on 27/May/19 $${if}\:{x}+\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{3}}.{find} \\ $$$${x}^{\mathrm{24}} +{x}^{\mathrm{18}} +{x}^{\mathrm{6}} +\mathrm{1} \\ $$ Answered by ajfour last updated on 27/May/19 $${E}={x}^{\mathrm{24}}…
Question Number 126430 by TITA last updated on 20/Dec/20 $$\mathrm{log}\:_{\mathrm{6}} ^{\mathrm{15}} =\mathrm{a}\:\:\:\mathrm{log}\:_{\mathrm{12}} ^{\mathrm{18}} =\mathrm{b}\:\:\mathrm{find}\:\mathrm{log}\:_{\mathrm{25}} ^{\mathrm{24}} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b} \\ $$ Commented by TITA last updated on…