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Question-119451

Question Number 119451 by help last updated on 24/Oct/20 Answered by Dwaipayan Shikari last updated on 24/Oct/20 $${x}=\mathrm{2},{y}=\mathrm{3}\:{z}=−\mathrm{4} \\ $$$${x}+{y}+{z}=\mathrm{1} \\ $$$${If}\:{you}\:{consider}\:{Complex}\:{solutions} \\ $$$${There}\:{will}\:{be}\:{infinite}\:{solutions} \\…

3-1-6-3-2-6-5-2-6-7-2-6-9-2-6-provet-that-

Question Number 184969 by SEKRET last updated on 14/Jan/23 $$\:\: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}\:+\:\frac{\mathrm{1}}{\mathrm{6}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{7}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{9}^{\mathrm{2}} }{\mathrm{6}+……}\:\:\:}\:\:}\:\:}\:\:\:\:}\:\:=\:\boldsymbol{\pi} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{provet}}\:\:\boldsymbol{\mathrm{that}}. \\ $$$$ \\…

If-are-the-three-roots-of-the-3x-3-12x-2-77x-11-0-find-the-value-of-1-1-1-

Question Number 119408 by ZiYangLee last updated on 24/Oct/20 $$\mathrm{If}\:\alpha,\beta,\gamma\:\mathrm{are}\:\mathrm{the}\:\mathrm{three}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{3}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} −\mathrm{77}{x}+\mathrm{11}=\mathrm{0}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\alpha−\mathrm{1}\right)\left(\beta−\mathrm{1}\right)\left(\gamma−\mathrm{1}\right). \\ $$ Commented by liberty last updated on 24/Oct/20…

The-length-of-a-rectangle-is-decreased-by-20-and-the-width-is-increased-by-x-but-the-area-remains-the-same-Find-the-value-of-x-

Question Number 119386 by ZiYangLee last updated on 24/Oct/20 $$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{decreased}\:\mathrm{by}\:\mathrm{20\%}, \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{width}\:\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:{x\%}, \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{area}\:\mathrm{remains}\:\mathrm{the}\:\mathrm{same}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}. \\ $$ Answered by mr W last updated on…

lim-x-0-e-x-e-x-2-x-2-let-x-2t-x-0-t-0-lim-x-0-e-x-e-x-2-x-2-lim-t-0-e-2t-e-2t-2-4t-2-1-4-lim-t-0-e-t-e-t-t-2-1-4-lim-t-0-

Question Number 184903 by aba last updated on 13/Jan/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }=?? \\ $$$$\mathrm{let}\:\mathrm{x}=\mathrm{2t}\:\begin{cases}{\mathrm{x}\rightarrow\mathrm{0}}\\{\mathrm{t}\rightarrow\mathrm{0}}\end{cases} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }=\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{2t}} +\mathrm{e}^{−\mathrm{2t}} −\mathrm{2}}{\mathrm{4t}^{\mathrm{2}}…

An-odd-function-f-x-whose-domain-is-R-satisfies-f-x-f-x-2-When-x-0-1-f-x-2x-2-ax-2-If-f-has-2023-zeros-in-0-1011-Then-the-range-of-a-can-be-A-6-2-2-B-4-2-2-C

Question Number 184872 by CrispyXYZ last updated on 13/Jan/23 $$\mathrm{An}\:\mathrm{odd}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{whose}\:\mathrm{domain}\:\mathrm{is}\:\mathbb{R} \\ $$$$\mathrm{satisfies}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right).\:\mathrm{When}\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right), \\ $$$${f}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{2}} +{ax}−\mathrm{2}. \\ $$$$\mathrm{If}\:{f}\:\mathrm{has}\:\mathrm{2023}\:\mathrm{zeros}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{1011}\right].\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{range}\:\mathrm{of}\:{a}\:\mathrm{can}\:\mathrm{be}\:? \\ $$$$\mathrm{A}.\:\left[−\mathrm{6},\:−\mathrm{2}\sqrt{\mathrm{2}}\right]\:\:\:\:\:\:\:\:\mathrm{B}.\:\left[−\mathrm{4},\:−\mathrm{2}\sqrt{\mathrm{2}}\right] \\ $$$$\mathrm{C}.\:\left[−\mathrm{8},\:−\mathrm{6}\right]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\left[−\mathrm{6},\:−\mathrm{4}\right] \\ $$…