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Author: Tinku Tara

If-x-y-z-xyz-Find-x-1-y-2-1-z-2-y-1-x-2-1-z-2-z-1-x-2-1-y-2-2xyz-

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-214483

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}…

a-b-c-d-e-f-Q-1-2-2-1-3-2-a-2-b-2-c-2-d-2-e-2-f-find-a-b-c-d-e-f-

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-214419

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}}…

Given-that-the-roots-of-the-equation-ax-2-bx-c-0-are-and-show-that-b-2-ac-2-where-Mr-Hans-

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…