Question Number 192134 by mustafazaheen last updated on 09/May/23 $$\mathrm{when}\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{7}} =\sqrt{\mathrm{57125}}+\sqrt{\mathrm{57124}} \\ $$$$\mathrm{then}\:\:\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{7}} =? \\ $$ Answered by som(math1967) last updated on 09/May/23 $$\:\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)=\mathrm{1} \\…
Question Number 192087 by Mastermind last updated on 07/May/23 $$\mathrm{Let}\:\left\{\mathrm{H}_{\alpha} \right\}\:\in\:\Omega,\:\mathrm{be}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\: \\ $$$$\mathrm{subgroup}\:\mathrm{of}\:\mathrm{a}\:\mathrm{group}\:\mathrm{G},\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\cap_{\alpha\:\in\:\Omega} \mathrm{H}_{\alpha} . \\ $$$$ \\ $$$$ \\ $$ Commented by…
Question Number 192062 by mehdee42 last updated on 07/May/23 $${prove}\:{it}\::\: \\ $$$$\:\:\:{times\_n}\:\:\:;\:\:\:\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+…+\sqrt{\mathrm{4}}}}\:\:}\:<\:\mathrm{3} \\ $$ Commented by ajfour last updated on 08/May/23 $${but}\:\mathrm{4}>\:\mathrm{3}\:\:\:\: \\ $$$${how}\:{can}\:{this}\:{be}… \\…
Question Number 192057 by Shrinava last updated on 07/May/23 $$\mathrm{Simplify}: \\ $$$$\frac{\sqrt{\mathrm{a}}\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{3}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{4}} }}{\left(\sqrt{\mathrm{a}}\:\:+\:\:\mathrm{1}\right)\centerdot\left(\mathrm{a}\:\:+\:\:\mathrm{1}\right)} \\ $$ Answered by mehdee42 last updated on 07/May/23 $$\:\:\:\frac{\sqrt{{a}}+{a}+{a}\sqrt{{a}}+{a}^{\mathrm{2}}…
Question Number 60980 by Tawa1 last updated on 28/May/19 $$\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…