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Question Number 184609 Answers: 2 Comments: 0
Question Number 184607 Answers: 0 Comments: 3
$${solve} \\ $$$$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{16}}\\{{y}^{\mathrm{2}} −{yz}+{z}^{\mathrm{2}} =\mathrm{25}}\\{{z}^{\mathrm{2}} −{zx}+{x}^{\mathrm{2}} =\mathrm{49}}\end{cases} \\ $$
Question Number 184602 Answers: 1 Comments: 1
Question Number 184600 Answers: 0 Comments: 3
Question Number 184594 Answers: 1 Comments: 0
$$\mathrm{If}\:{f}\left({x}\right)=\mathrm{ln}\mid{a}+\frac{\mathrm{1}}{\mathrm{1}−{x}}\mid+{b}\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a},\:{b}. \\ $$
Question Number 184590 Answers: 0 Comments: 0
Question Number 184574 Answers: 0 Comments: 5
$$\mathrm{Test}\:\mathrm{whether}\:\mathrm{this}\:\mathrm{is}\:\mathrm{Convergent}\:\mathrm{or} \\ $$$$\mathrm{Divergent} \\ $$$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{n}!\mathrm{x}^{\mathrm{n}} }{\mathrm{5n}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$
Question Number 184573 Answers: 4 Comments: 2
Question Number 184567 Answers: 1 Comments: 0
$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$$\sqrt{{a}}\:\:+\sqrt{{b}}\:={z}\:\:\:\:\left({a},{b},{z}\right)\in\mathbb{N}^{\mathrm{3}} \\ $$$${a},{b}\:? \\ $$
Question Number 184557 Answers: 1 Comments: 1
$${Determiner} \\ $$$$\mathrm{1}\bullet\mathrm{AB},\:\:\mathrm{BC}\:\:\mathrm{AC}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\boldsymbol{\mathrm{r}} \\ $$$$\mathrm{2}\bullet\:\:\measuredangle\mathrm{CBA}\:;\:\:\measuredangle\mathrm{BAC}\:;{et}\:\measuredangle\mathrm{BCA} \\ $$
Question Number 184555 Answers: 3 Comments: 6
$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{complex}\:\mathrm{numbers}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{or}\:\boldsymbol{\mathrm{y}}\:\mathrm{is}\:\mathrm{7}\:,\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{cubes}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{largest} \\ $$$$\mathrm{true}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{these}\:\mathrm{conditions}. \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{4}\left.\:\left.\:\:\mathrm{B}\right)\mathrm{5}\:\:\:\mathrm{C}\right)\mathrm{6}\:\:\:\mathrm{D}\right)\mathrm{7}\:\:\:\mathrm{E}\right)\mathrm{8} \\ $$
Question Number 184552 Answers: 2 Comments: 0
$${I}_{\mathrm{1}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}−\frac{\sqrt{\mathrm{2}}}{\:\sqrt{{x}}}\right){dx}=? \\ $$$${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}−\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{2}}}\right){dx}=? \\ $$
Question Number 184551 Answers: 1 Comments: 0
$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$${x}+{y}+\sqrt{{xy}}\:\:\:\:=\mathrm{39} \\ $$
Question Number 184538 Answers: 1 Comments: 1
$$ \\ $$
Question Number 184535 Answers: 6 Comments: 0
$$\mathrm{If}\:{a},\:{b}>\mathrm{0}\:\mathrm{such}\:\mathrm{that}\:\mathrm{2}{a}+{b}=\mathrm{2}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}: \\ $$$$\left.\mathrm{1}\right)\:\:\left(\mathrm{4}{a}^{\mathrm{2}} +\mathrm{1}\right)\left({b}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:\:\frac{\mathrm{2}{a}^{\mathrm{2}} −{b}+\mathrm{4}}{{a}+\mathrm{1}}+\frac{{b}^{\mathrm{2}} −\mathrm{2}{a}−\mathrm{2}}{{b}+\mathrm{4}} \\ $$
Question Number 184523 Answers: 2 Comments: 0
Question Number 184514 Answers: 1 Comments: 0
Question Number 184511 Answers: 0 Comments: 0
$${In}\:{a}\:{regular}\:{heptagon}\:{ABCDEFG}\:: \\ $$$$\:\sqrt{\mathrm{2}\left({AC}\right)^{\mathrm{2}} −\left({AD}\right)^{\mathrm{2}} }\:−\:{AD}\:=\:\mathrm{2} \\ $$$$\:{find}\:{BC}.\: \\ $$
Question Number 184505 Answers: 1 Comments: 0
$$\:\:\:\frac{\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)^{\mathrm{5}} −\boldsymbol{\mathrm{a}}^{\mathrm{5}} −\boldsymbol{\mathrm{b}}^{\mathrm{5}} −\boldsymbol{\mathrm{c}}^{\mathrm{5}} }{\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)^{\mathrm{3}} −\boldsymbol{\mathrm{a}}^{\mathrm{3}} −\boldsymbol{\mathrm{b}}^{\mathrm{3}} −\boldsymbol{\mathrm{c}}^{\mathrm{3}} }\:=\:? \\ $$$$\:\mathrm{is}\:\mathrm{there}\:{an}\:\:{easier}\:\:{way}. \\ $$
Question Number 184503 Answers: 1 Comments: 0
Question Number 184497 Answers: 1 Comments: 0
Question Number 184492 Answers: 1 Comments: 2
Question Number 184490 Answers: 2 Comments: 1
Question Number 184487 Answers: 0 Comments: 1
Question Number 184481 Answers: 2 Comments: 0
Question Number 184478 Answers: 1 Comments: 0
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