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Category: Algebra

5-1-6-2-7-3-8-4-

Question Number 195435 by universe last updated on 02/Aug/23 $$\sqrt{\mathrm{5}+\mathrm{1}\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{8}+\mathrm{4}\sqrt{…}}}}}\:\:=\:\:\:? \\ $$ Answered by mr W last updated on 02/Aug/23 $$\mathrm{3}=\sqrt{\mathrm{9}}=\sqrt{\mathrm{5}+\mathrm{4}} \\ $$$$\mathrm{4}=\mathrm{1}×\mathrm{4}=\mathrm{1}×\sqrt{\mathrm{16}}=\mathrm{1}×\sqrt{\mathrm{6}+\mathrm{10}} \\ $$$$\mathrm{10}=\mathrm{2}×\mathrm{5}=\mathrm{2}×\sqrt{\mathrm{25}}=\mathrm{2}×\sqrt{\mathrm{7}+\mathrm{18}}…

Question-195404

Question Number 195404 by universe last updated on 01/Aug/23 Answered by AST last updated on 01/Aug/23 $$\left(\frac{\mathrm{127}^{\mathrm{2}} }{{xy}}+\frac{{x}}{{y}}+\frac{{y}}{{x}}\right)\left(\mathrm{127}+{x}+{y}\right) \\ $$$$=\frac{\mathrm{127}^{\mathrm{3}} }{{xy}}+\frac{\mathrm{127}^{\mathrm{2}} }{{y}}+\frac{\mathrm{127}^{\mathrm{2}} }{{x}}+\frac{\mathrm{127}{x}}{{y}}+\frac{{x}^{\mathrm{2}} }{{y}}+{x}+\frac{\mathrm{127}{y}}{{x}}+{y}+\frac{{y}^{\mathrm{2}} }{{x}}…

f-2-g-2-g-2-2-then-find-the-fog-2-

Question Number 195407 by mustafazaheen last updated on 01/Aug/23 $$\mathrm{f}'\left(\mathrm{2}\right)=\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{g}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=? \\ $$ Answered by gatocomcirrose last updated on 01/Aug/23 $$\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=\mathrm{f}'\left(\mathrm{g}\left(\mathrm{2}\right)\right)\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{2f}'\left(\mathrm{2}\right)=\mathrm{4} \\ $$ Answered…

Question-195357

Question Number 195357 by SirMUTUKU last updated on 31/Jul/23 Answered by Spillover last updated on 31/Jul/23 $$\frac{{E}}{\mathrm{1}−\pi}=\sqrt{\frac{{h}−\mathrm{0}.\mathrm{5}}{\mathrm{1}−{h}}}\: \\ $$$$\left(\frac{{E}}{\mathrm{1}−\pi}\right)^{\mathrm{2}} =\frac{{h}−\mathrm{0}.\mathrm{5}}{\mathrm{1}−{h}} \\ $$$$\frac{{E}^{\mathrm{2}} }{\left(\mathrm{1}−\pi\right)^{\mathrm{2}} }=\frac{{h}−\mathrm{0}.\mathrm{5}}{\mathrm{1}−{h}} \\…

remark-to-question-195301-and-similar-ones-x-2-y-a-x-y-2-b-a-b-gt-0-how-many-solutions-depending-on-a-b-

Question Number 195356 by MJS_new last updated on 31/Jul/23 $$\mathrm{remark}\:\mathrm{to}\:\mathrm{question}\:\mathrm{195301}\:\mathrm{and}\:\mathrm{similar}\:\mathrm{ones} \\ $$$${x}^{\mathrm{2}} +{y}={a} \\ $$$${x}+{y}^{\mathrm{2}} ={b} \\ $$$${a},\:{b}\:>\mathrm{0} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{depending}\:\mathrm{on}\:{a},\:{b}? \\ $$ Answered by MJS_new…

Question-195369

Question Number 195369 by Shlock last updated on 31/Jul/23 Answered by witcher3 last updated on 01/Aug/23 $$\mathrm{x}=−\mathrm{y} \\ $$$$\Rightarrow\mathrm{f}\left(\mathrm{f}\left(\mathrm{0}\right)\right)=\mathrm{2f}\left(\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{2}}\mathrm{f}\left(\mathrm{f}\left(\mathrm{0}\right)\right)=\mathrm{f}\left(\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\forall\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{Z}\:^{\mathrm{2}}…