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Category: Algebra

If-x-y-z-15-and-xy-yz-zx-85-find-x-2-y-2-z-2-

Question Number 50710 by Tawa1 last updated on 19/Dec/18 $$\mathrm{If}\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{15}\:\:\mathrm{and}\:\:\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}\:\:=\:\mathrm{85},\:\:\:\mathrm{find}\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \\ $$ Answered by mr W last updated on 19/Dec/18 $$\left({x}+{y}+{z}\right)^{\mathrm{2}} =\left({x}+{y}\right)^{\mathrm{2}} +\mathrm{2}\left({x}+{y}\right){z}+{z}^{\mathrm{2}}…

1-2-2-1-3-2-2-3-1-4-3-3-4-1-100-99-99-100-

Question Number 116226 by bobhans last updated on 02/Oct/20 $$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}}\:+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+…+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$ Commented by bemath last updated on 02/Oct/20 $$\mathrm{0}.\mathrm{9} \\ $$ Answered by john…

Given-and-are-the-roots-of-x-3-px-2-qx-pq-0-Find-the-value-of-

Question Number 116221 by bobhans last updated on 02/Oct/20 $$\mathrm{Given}\:\alpha,\beta\:\mathrm{and}\:\varphi\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\mathrm{x}^{\mathrm{3}} −\mathrm{px}^{\mathrm{2}} +\mathrm{qx}−\mathrm{pq}\:=\:\mathrm{0}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\alpha}{\beta}+\frac{\beta}{\alpha}+\frac{\beta}{\varphi}+\frac{\varphi}{\beta}+\frac{\alpha}{\varphi}+\frac{\varphi}{\alpha}=? \\ $$ Answered by TANMAY PANACEA last updated on…

Prove-that-X-t-1-1-t-2-LN-1-1-t-2-t-Y-t-t-1-t-2-function-is-the-solution-of-the-following-equation-y-1-y-2-y-

Question Number 181751 by Shrinava last updated on 29/Nov/22 $$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\begin{cases}{\mathrm{X}\left(\mathrm{t}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:\mathrm{t}^{\mathrm{2}} }}\:−\mathrm{LN}\:\frac{\mathrm{1}\:+\:\sqrt{\mathrm{1}\:+\:\mathrm{t}^{\mathrm{2}} }}{\mathrm{t}}}\\{\mathrm{Y}\left(\mathrm{t}\right)\:=\:\frac{\mathrm{t}}{\:\sqrt{\mathrm{1}\:+\:\mathrm{t}^{\mathrm{2}} }}}\end{cases} \\ $$$$\mathrm{function}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{equation}: \\ $$$$\mathrm{y}\:\sqrt{\mathrm{1}\:+\:\mathrm{y}'^{\mathrm{2}} }\:=\:\mathrm{y}^{'} \\ $$ Terms…

Question-181749

Question Number 181749 by Shrinava last updated on 29/Nov/22 Answered by Frix last updated on 30/Nov/22 $$\mathrm{A}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\left({a},\:{b}\right)\:\mathrm{if} \\ $$$$\forall{c}\in\left({a},{b}\right) \\ $$$$\mathrm{1}.\:{f}\left({c}\right)\:\mathrm{is}\:\mathrm{defined}\:\left[\mathrm{it}\:\mathrm{has}\:\mathrm{no}\:\mathrm{gaps}\right] \\ $$$$\mathrm{2}.\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}{f}\left({x}\right)={f}\left({c}\right)\:\left[\mathrm{it}\:\mathrm{doesn}'\mathrm{t}\:“\mathrm{jump}''\right] \\…

How-many-ways-can-the-letters-of-the-word-DENKENMATHEMATICAL-be-arranged-if-no-same-letters-must-be-together-

Question Number 116173 by I want to learn more last updated on 01/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{DENKENMATHEMATICAL} \\ $$$$\mathrm{be}\:\mathrm{arranged}\:\mathrm{if}\:\mathrm{no}\:\mathrm{same}\:\mathrm{letters}\:\mathrm{must}\:\mathrm{be}\:\mathrm{together} \\ $$ Commented by mr W last updated on…