Question Number 50328 by peter frank last updated on 15/Dec/18 Answered by peter frank last updated on 16/Dec/18 $$\left.\mathrm{1}\right) \\ $$$${x}+\mathrm{2}{y}−\mathrm{3}{z}={a}…\left({i}\right) \\ $$$$\mathrm{2}{x}+\mathrm{6}{y}−\mathrm{11}{z}={b}…\left({ii}\right) \\ $$$${x}−\mathrm{2}{y}+\mathrm{7}{z}={c}….\left({iii}\right)…
Question Number 115858 by bemath last updated on 29/Sep/20 $${What}\:{are}\:{all}\:{ordered}\:{pairs}\:{of}\:{real} \\ $$$${number}\:\left({x},{y}\right)\:{for}\:{which}\: \\ $$$$\mathrm{5}^{{y}−{x}} \:\left({x}+{y}\right)\:=\:\mathrm{1}\:{and}\:\left({x}+{y}\right)^{{x}−{y}} \:=\:\mathrm{5} \\ $$ Answered by floor(10²Eta[1]) last updated on 29/Sep/20…
Question Number 115857 by bemath last updated on 29/Sep/20 $${What}\:{are}\:{all}\:{real}\:{values}\:{of}\:{p}\:{for} \\ $$$${which}\:{the}\:{inequality}\: \\ $$$$−\mathrm{3}<\frac{{x}^{\mathrm{2}} +{px}−\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}<\mathrm{2}\:{is}\:{satisfied}\: \\ $$$${by}\:{all}\:{real}\:{values}\:{of}\:{x} \\ $$ Answered by bobhans last updated…
Question Number 181375 by Tawa11 last updated on 24/Nov/22 $$\mathrm{If}\:\:\mathrm{a}\:=\:\mathrm{1},\:\mathrm{b}\:=\:\mathrm{2},\:\mathrm{c}\:=\:\mathrm{3},\:…\:\mathrm{z}\:\:=\:\:\mathrm{26} \\ $$$$\mathrm{then}\:\:\:\:\left(\mathrm{t}\:−\:\mathrm{a}\right)\left(\mathrm{t}\:−\:\mathrm{b}\right)\left(\mathrm{t}\:−\:\mathrm{c}\right)\:…\:\left(\mathrm{t}\:−\:\mathrm{y}\right)\left(\mathrm{t}\:−\:\mathrm{z}\right)\:=\:\:\:?? \\ $$ Commented by mr W last updated on 24/Nov/22 $$\:…\:\:{is}\:\left({t}−{d}\right)…\left({t}−{s}\right)\left({t}−{t}\right)\left({t}−{u}\right)…\left({t}−{x}\right) \\ $$…
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Question Number 115815 by Ar Brandon last updated on 28/Sep/20 $$\mathrm{Montrer}\:\mathrm{que}\:\:\forall\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)\in\left(\mathbb{R}_{+} ^{\ast} \right)^{\mathrm{3}} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} +\mathrm{bc}}+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} +\mathrm{ac}}+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{2}} +\mathrm{ab}}\leqslant\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{ab}}+\frac{\mathrm{1}}{\mathrm{bc}}+\frac{\mathrm{1}}{\mathrm{ac}}\right) \\ $$ Answered by 1549442205PVT last updated…
Question Number 50279 by Saorey last updated on 15/Dec/18 $$\begin{cases}{\mathrm{x}+\mathrm{y}=\mathrm{6}}\\{\mathrm{y}+\mathrm{z}=\mathrm{10}}\end{cases}\:\:\left(\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\right) \\ $$ Answered by mr W last updated on 15/Dec/18 $${if}\:{x},{y},{z}\:{are}\:{integers},{then} \\ $$$$\left({x},{y},{z}\right)=\left(\mathrm{1},\mathrm{5},\mathrm{5}\right)/\left(\mathrm{2},\mathrm{4},\mathrm{6}\right)/\left(\mathrm{3},\mathrm{3},\mathrm{7}\right)/\left(\mathrm{4},\mathrm{2},\mathrm{8}\right)/\left(\mathrm{5},\mathrm{1},\mathrm{9}\right) \\ $$$${if}\:{x},{y},{z}\:{are}\:{real},\:{then}…
Question Number 50278 by LYCON TRIX last updated on 15/Dec/18 $$\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}\:+\:\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}\:=\:\mathrm{2x} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{beg}\:\mathrm{u}\:\mathrm{guys}\: \\ $$$$\mathrm{please}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$ Commented by ajfour last updated on 15/Dec/18 $${a}\:{and}\:{x}\:\in\:\mathbb{R}\:\:{or}\:\mathbb{C}\:?…
Question Number 181318 by mr W last updated on 23/Nov/22 $${if}\:{x}+{y}+{z}=\mathrm{0},\:{find}\:{the}\:{maximum}\:{of} \\ $$$$\frac{\mid{x}+\mathrm{2}{y}+\mathrm{3}{z}\mid}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}. \\ $$ Commented by mr W last updated on…
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