Question Number 50717 by Tawa1 last updated on 19/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Dec/18 $${x}+\sqrt{{y}}\:−\sqrt{{x}}\:−{y}=\mathrm{4} \\ $$$$\left(\sqrt{{x}}+\sqrt{{y}}\:\right)\left(\sqrt{{x}}\:−\sqrt{{y}}\:\right)−\left(\sqrt{{x}}\:−\sqrt{{y}}\:\right)=\mathrm{4} \\ $$$$\left(\sqrt{{x}}\:−\sqrt{{y}}\:\right)\left(\sqrt{{x}}\:+\sqrt{{y}}\:−\mathrm{1}\right)=\mathrm{4} \\ $$$$\:{by}\:{logic}\:{trial}\:{x}=\mathrm{9}\:\:{y}=\:\mathrm{4}\:\:{so}\:\:\:{z}=\mathrm{1} \\ $$$$…
Question Number 116253 by I want to learn more last updated on 02/Oct/20 $$\left(\mathrm{1}\right)\:\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\underset{\mathrm{i}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{L}_{\mathrm{i}} \left(\mathrm{x}\right)\:\:\:=\:\:\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\underset{\mathrm{i}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{L}_{\mathrm{i}} \left(\mathrm{x}\right).\:\mathrm{x}_{\mathrm{i}} ^{\mathrm{k}} \:\:\:=\:\:\:\mathrm{x}^{\mathrm{k}} ,\:\:\:\:\:\:\:\:\mathrm{k}\:\leqslant\:\mathrm{n}…
Question Number 50710 by Tawa1 last updated on 19/Dec/18 $$\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}}…
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Question Number 50698 by Cheyboy last updated on 19/Dec/18 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$ \\ $$$$\mathrm{4}^{\mathrm{2x}+\mathrm{1}} ×\mathrm{5}^{\mathrm{x}−\mathrm{2}} =\:\mathrm{6}^{\mathrm{1}−\mathrm{x}} \\ $$ Answered by MJS last updated on 19/Dec/18…
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…
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…
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 Number 181749 by Shrinava last updated on 29/Nov/22 Answered by Frix last updated on 30/Nov/22 $$\mathrm{A}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\left({a},\:{b}\right)\:\mathrm{if} \\ $$$$\forall{c}\in\left({a},{b}\right) \\ $$$$\mathrm{1}.\:{f}\left({c}\right)\:\mathrm{is}\:\mathrm{defined}\:\left[\mathrm{it}\:\mathrm{has}\:\mathrm{no}\:\mathrm{gaps}\right] \\ $$$$\mathrm{2}.\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}{f}\left({x}\right)={f}\left({c}\right)\:\left[\mathrm{it}\:\mathrm{doesn}'\mathrm{t}\:“\mathrm{jump}''\right] \\…
Question Number 116192 by bemath last updated on 01/Oct/20 Commented by MJS_new last updated on 01/Oct/20 $${x}={y}={z}=\mathrm{0} \\ $$$$\mathrm{not}\:\mathrm{sure}\:\mathrm{how}\:\mathrm{to}\:\mathrm{further}\:\mathrm{solve}\:\mathrm{it} \\ $$ Answered by TANMAY PANACEA…