Question Number 214455 by hardmath last updated on 09/Dec/24 $$\mathrm{If}\:\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{z}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{2xyz}} \\ $$ Commented by Ghisom…
Question Number 214483 by MATHEMATICSAM last updated on 09/Dec/24 Answered by ajfour last updated on 09/Dec/24 $${let}\:{C}\equiv\left({h},\:\mathrm{2}−{r}\right) \\ $$$$\left({x}−{h}\right)^{\mathrm{2}} +\left({mx}^{\mathrm{2}} −\mathrm{2}+{r}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\frac{{h}−{x}}{{mx}^{\mathrm{2}} −\mathrm{2}+{r}}=\mathrm{2}{mx}…
Question Number 214447 by 2universe456 last updated on 08/Dec/24 Commented by Frix last updated on 08/Dec/24 $$={abc} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 214443 by hardmath last updated on 08/Dec/24 $$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:\in\:\mathrm{Q} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{2}}}\:=\:\mathrm{2}^{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{c}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{d}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{e}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{f}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:=\:? \\ $$ Answered by ajfour last…
Question Number 214427 by ajfour last updated on 08/Dec/24 Commented by ajfour last updated on 08/Dec/24 https://youtu.be/pnMSZ77i2P8?si=OaLd0p_DlkwNYv8d Answered by a.lgnaoui last updated on 08/Dec/24 $$\mathrm{Resolution}\:\mathrm{de}\:\mathrm{l}\:\mathrm{equation}\:\mathrm{donne}…
Question Number 214421 by ChantalYah last updated on 08/Dec/24 Answered by TonyCWX08 last updated on 08/Dec/24 $${Use}\:{Newton}'{s}\:{Identity} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 214448 by jahar last updated on 08/Dec/24 $$ \\ $$$$\overset{−} {{x}}\:=\:\frac{\Sigma{f}_{{i}} {x}_{{i}} }{\Sigma{f}_{{i}} \:}\:,\:\:\:\overset{−} {{u}}\:=\:\frac{\Sigma{f}_{{i}} {u}_{{i}} }{\Sigma{f}_{{i}} }\:,\:{u}\:=\:\frac{{x}−{a}}{{h}}\:, \\ $$$${proved}\:{that}\:\overset{−} {{x}}\:=\:{a}\:+\:{h}\overset{−} {{u}} \\…
Question Number 214449 by ajfour last updated on 08/Dec/24 Commented by ajfour last updated on 09/Dec/24 https://youtu.be/mVW8FiNpKjk?si=q68kdETxCuqwyZ3- Answered by mr W last updated on 14/Dec/24…
Question Number 214419 by 2universe456 last updated on 08/Dec/24 Answered by golsendro last updated on 08/Dec/24 $$\:\:\:\:\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{2xy}=\mathrm{25}}\\{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{47}=\mathrm{10xy}}\end{cases}\Rightarrow\mathrm{2xy}+\mathrm{47}=\mathrm{10xy}+\mathrm{25} \\ $$$$\:\:\:\mathrm{8xy}=\:\mathrm{22}\Rightarrow\mathrm{4xy}=\mathrm{11} \\ $$$$\:\:\:\mathrm{4x}\left(\mathrm{5}−\mathrm{x}\right)=\mathrm{11}\:\Rightarrow\mathrm{4x}^{\mathrm{2}}…
Question Number 214414 by ChantalYah last updated on 07/Dec/24 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\:\beta, \\ $$$$\:\mathrm{show}\:\mathrm{that}; \\ $$$$\lambda\mu\mathrm{b}^{\mathrm{2}} =\mathrm{ac}\left(\lambda+\mu\right)^{\mathrm{2}} \:\mathrm{where}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Mr}\:{Hans} \\ $$ Answered by…