Menu Close

Category: Algebra

5y-2-2axy-b-0-ay-2-2bx-5c-0-5x-3a-y-2-4ax-2-y-bx-5c-0-5y-2-x-5x-2a-y-ax-3-3b-0-Please-solve-simultaneously-for-x-and-y-such-that-all-four-equations-are-obeyed-

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} \\…

1-z-a-bi-2-z-re-i-express-the-values-of-a-real-z-z-real-part-b-imag-z-z-imaginary-part-c-abs-z-z-absolute-value-d-arg-z-z-argument-angle-

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}}…

Prove-or-disprove-that-for-even-positive-n-2-k-1-n-2-1-1-k-n-k-1-n-2-n-n-2-2-2-

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…

find-x-in-terms-of-a-1-x-2x-x-2-1-x-2x-x-2-a-3-2-x-x-2-x-x-

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}}…

if-x-2-5x-9-0-then-x-

Question Number 2304 by Ashis last updated on 14/Nov/15 $${if}\:\:{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{9}=\:\mathrm{0}\:\:{then}\:{x}=? \\ $$ Answered by prakash jain last updated on 14/Nov/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{9} \\ $$$${x}=\frac{−\mathrm{5}\pm\sqrt{\left(−\mathrm{5}\right)^{\mathrm{2}}…