Question Number 133612 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{If}\:\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{2z}=\mathrm{k}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{z}=\mathrm{k}}\\{\mathrm{2x}+\mathrm{y}+\mathrm{z}=\mathrm{k}}\end{cases}\:;\:\mathrm{k}\neq\:\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:=? \\ $$$$ \\ $$ Commented by mr W last updated…
Question Number 68063 by TawaTawa last updated on 04/Sep/19 Answered by MJS last updated on 04/Sep/19 $$\mathrm{tricky}\:\mathrm{but}\:\mathrm{easy} \\ $$$$\left(\mathrm{1}\right)\:\:{x}^{\mathrm{3}} −\mathrm{3}{y}^{\mathrm{2}} {x}={a}+\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:{y}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}={a}…
Question Number 133568 by bemath last updated on 23/Feb/21 $$\mathrm{Proof}\:\mathrm{the}\:\mathrm{series}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}}{\mathrm{9}+\mathrm{2n}\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{2}} } \\ $$$$\mathrm{convergent} \\ $$$$ \\ $$ Answered by EDWIN88 last updated on…
Question Number 133542 by help last updated on 22/Feb/21 Commented by help last updated on 22/Feb/21 $${x}^{\mathrm{3}{n}+\mathrm{2}} +{x}+\mathrm{1}\:\:{is}\:{divisible}\:{by}\:{x}^{\mathrm{2}} +{x}+\mathrm{1} \\ $$$${correct}\:{question} \\ $$ Terms of…
Question Number 67997 by ajfour last updated on 03/Sep/19 $$\mathrm{5}{y}^{\mathrm{2}} +\mathrm{2}{axy}+{b}=\mathrm{0} \\ $$$${ay}^{\mathrm{2}} +\mathrm{2}{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\left(\mathrm{5}{x}+\mathrm{3}{a}\right){y}^{\mathrm{2}} +\left(\mathrm{4}{ax}^{\mathrm{2}} \right){y}−{bx}−\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{5}{y}^{\mathrm{2}} −{x}\left(\mathrm{5}{x}+\mathrm{2}{a}\right){y}−{ax}^{\mathrm{3}} −\mathrm{3}{b}=\mathrm{0} \\ $$$${Please}\:{solve}\:{simultaneously} \\…
Question Number 67992 by MJS last updated on 03/Sep/19 $$\left(\mathrm{1}\right)\:{z}={a}+{b}\mathrm{i} \\ $$$$\left(\mathrm{2}\right)\:{z}={r}\mathrm{e}^{\mathrm{i}\theta} \\ $$$$\mathrm{express}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{real}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{real}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{b}\right)\:\mathrm{imag}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{imaginary}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{c}\right)\:\mathrm{abs}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{absolute}\:\mathrm{value}\right] \\ $$$$\left(\mathrm{d}\right)\:\mathrm{arg}\:\left({z}^{{z}}…
Question Number 2454 by Yozzi last updated on 20/Nov/15 $${Find}\:{smallest}\:{a}>\mathrm{1}\:{for}\:{which} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}+{sinx}}{{a}+{siny}}\leqslant{e}^{{y}−{x}} \\ $$$${for}\:\forall\:{x}\leqslant{y}. \\ $$ Commented by Rasheed Soomro last updated on 21/Nov/15 $${Find}\:{smallest}\:{a}>\mathrm{1}\:{for}\:{which}…
Question Number 2441 by Yozzi last updated on 20/Nov/15 $${Prove}\:{or}\:{disprove}\:{that}\:,\:{for}\:{even}\: \\ $$$${positive}\:{n}, \\ $$$$\mathrm{2}×\underset{{k}=\mathrm{1}} {\overset{\frac{{n}}{\mathrm{2}}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}+\left(−\mathrm{1}\right)^{\left({n}/\mathrm{2}\right)} \frac{{n}!}{\left(\left({n}/\mathrm{2}\right)!\right)^{\mathrm{2}} }=−\mathrm{2} \\ $$ Commented by Rasheed Soomro…
Question Number 133469 by Eric002 last updated on 22/Feb/21 $${find}\:{x}\:{in}\:{terms}\:{of}\:{a} \\ $$$$\frac{\mathrm{1}+{x}−\sqrt{\mathrm{2}{x}+{x}^{\mathrm{2}} }}{\mathrm{1}+{x}+\sqrt{\mathrm{2}{x}+{x}^{\mathrm{2}} }}={a}^{\mathrm{3}} \frac{\sqrt{\mathrm{2}+{x}}+\sqrt{{x}}}{\:\sqrt{\mathrm{2}+{x}}−\sqrt{{x}}} \\ $$ Answered by EDWIN88 last updated on 22/Feb/21 $$\frac{\left[\left(\mathrm{1}+\mathrm{x}\right)−\sqrt{\mathrm{2x}+\mathrm{x}^{\mathrm{2}}…
Question Number 133450 by Gap last updated on 22/Feb/21 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com