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A-1-A-2-A-3-A-n-are-defined-as-follows-A-1-2-A-n-1-2-A-1-A-2-A-3-A-n-for-n-1-2-3-a-Evaluate-the-numerical-values-of-A-3-and-A-4-b-Prove-that-A-2-A-3-A-n-form-a-geome

Question Number 122999 by ZiYangLee last updated on 21/Nov/20 $${A}_{\mathrm{1}} ,{A}_{\mathrm{2}} ,{A}_{\mathrm{3}} ,\ldots,{A}_{{n}} \:\mathrm{are}\:\mathrm{defined}\:\mathrm{as}\:\mathrm{follows} \\ $$$$\:\:\:\:{A}_{\mathrm{1}} =\mathrm{2},\:{A}_{{n}−\mathrm{1}} =\mathrm{2}\left({A}_{\mathrm{1}} +{A}_{\mathrm{2}} +{A}_{\mathrm{3}} +\ldots+{A}_{{n}} \right) \\ $$$${for}\:{n}=\mathrm{1},\mathrm{2},\mathrm{3},\ldots \\…

Question-122995

Question Number 122995 by danielasebhofoh last updated on 21/Nov/20 Commented by MJS_new last updated on 22/Nov/20 $$\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:\mathrm{the}\:\mathrm{simultaneous} \\ $$$$\mathrm{equations} \\ $$ Answered by mohammad17 last…

x-3-y-3-z-3-3xyz-x-y-z-x-2-y-2-z-2-xy-yz-zx-if-x-y-z-0-then-x-3-y-3-z-3-3xyz-0-x-2-y-2-z-2-xy-yz-zx-0-

Question Number 188512 by vishal1234 last updated on 02/Mar/23 $${x}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{3}} +\boldsymbol{{z}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{xyz}}= \\ $$$$\left(\boldsymbol{{x}}+\boldsymbol{{y}}+\boldsymbol{{z}}\right)\:\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} −\boldsymbol{{xy}}−\boldsymbol{{yz}}−\boldsymbol{{zx}}\right) \\ $$$$\boldsymbol{{if}}\:\boldsymbol{{x}}+\boldsymbol{{y}}+\boldsymbol{{z}}\:=\:\mathrm{0},\:{then} \\ $$$${x}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{3}} +\boldsymbol{{z}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{xyz}}…

Question-57433

Question Number 57433 by naka3546 last updated on 04/Apr/19 Answered by tanmay.chaudhury50@gmail.com last updated on 04/Apr/19 $$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} \left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}}{dx} \\ $$$$\int\frac{{x}+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }}{\:\sqrt{{x}^{\mathrm{2}}…