Question Number 126552 by mathocean1 last updated on 21/Dec/20 $${u}\:;\:{v}\in\:\mathbb{C}\:{such}\:{that}\:\mid{u}\mid=\mid{v}\mid=\mathrm{1} \\ $$$${and}\:{uv}\neq−\mathrm{1}. \\ $$$${show}\:{that}\:\frac{{u}+{v}}{\mathrm{1}+{uv}}\:\in\:\mathbb{R}. \\ $$ Answered by Olaf last updated on 21/Dec/20 $${u}\:=\:{e}^{{i}\alpha} ,\:{v}\:=\:{e}^{{i}\beta}…
Question Number 126553 by mathocean1 last updated on 21/Dec/20 $${show}\:{thatfor}\:{z}\in\mathbb{C}\: \\ $$$$\mid{z}+\mathrm{1}\mid^{\mathrm{2}} =\mathrm{2}\mid{z}\mid^{\mathrm{2}\:} \Leftrightarrow\mid{z}−\mathrm{1}\mid^{\mathrm{2}} =\mathrm{2}. \\ $$$${This}\:{formula}\:{can}\:{be}\:{used}: \\ $$$$\mid{z}\mid^{\mathrm{2}} ={z}×\overset{−} {{z}} \\ $$ Answered by…
Question Number 192084 by sciencestudentW last updated on 07/May/23 $${f}\left({x}\right)+{x}\centerdot{f}\left(−{x}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${f}\left(\sqrt{\mathrm{2}}\right)=? \\ $$ Answered by AST last updated on 07/May/23 $${x}^{\mathrm{2}} +\mathrm{1}=−\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}\right)+\mathrm{2}=−\left(\mathrm{1}+{x}−{x}\left(\mathrm{1}+{x}\right)\right)+\mathrm{2} \\…
Question Number 192080 by sciencestudentW last updated on 07/May/23 $${f}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} \:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)+{f}\left(\mathrm{8}\right)=? \\ $$ Answered by AST last updated on 07/May/23 $${f}^{−\mathrm{1}}…
Question Number 126549 by mohammad17 last updated on 21/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192083 by sciencestudentW last updated on 07/May/23 $${f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${f}\left({x}−\mathrm{1}\right)+{f}\left({x}\right)+{f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=? \\ $$ Answered by AST last updated on 07/May/23…
Question Number 126542 by MathSh last updated on 21/Dec/20 $$\mathrm{17}^{\mathrm{202}} \\ $$$${the}\:{end}\:\:\mathrm{3}\:{number}? \\ $$ Commented by AlagaIbile last updated on 21/Dec/20 Answered by Olaf last…
Question Number 192076 by sciencestudentW last updated on 07/May/23 $${f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}\:\:\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by AST last updated on 07/May/23 $${y}={f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\…
Question Number 126538 by Ndala last updated on 21/Dec/20 $${if}\:\:{a}+{b}\geqslant{c}>\mathrm{0} \\ $$$${Prove}\:{that}\:\frac{{a}}{\mathrm{1}+{a}}+\frac{{b}}{\mathrm{1}+{b}}>\frac{{c}}{\mathrm{1}+{c}} \\ $$$$. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help},\:\mathrm{please}! \\ $$ Commented by MJS_new last updated on 21/Dec/20…
Question Number 126536 by mathocean1 last updated on 21/Dec/20 $${show}\:{by}\:{recurrence}\:{that} \\ $$$$\forall\:{integer}\:{p}\geqslant\mathrm{4},\:\left({p}+\mathrm{1}\right)^{\mathrm{3}} \leqslant\mathrm{3}{p}^{\mathrm{3}} \\ $$$$ \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…