Category: Algebra

Question Number 116323 by bobhans last updated on 03/Oct/20 $$\left(1\right)\mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{real}\mathrm{number}\mathrm{such}\mathrm{that}$$$$\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}=\frac{1}{3},\frac{\mathrm{bc}}{\mathrm{b}+\mathrm{c}}=\frac{1}{4}\mathrm{and}\frac{\mathrm{ac}}{\mathrm{a}+\mathrm{c}}=\frac{1}{5}.\mathrm{Find}$$$$\mathrm{the}\mathrm{value}\mathrm{of}\frac{24\mathrm{abc}}{\mathrm{ab}+\mathrm{ac}+\mathrm{bc}}?$$$$\left(2\right)\mathrm{Let}\mathrm{p}\mathrm{and}\mathrm{q}\mathrm{be}\mathrm{two}\mathrm{real}\mathrm{number}\mathrm{that}$$$$\mathrm{satisfy}\mathrm{p}.\mathrm{q}=2013.\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{minimum}$$$$\mathrm{value}\mathrm{of}{(\mathrm{p}+\mathrm{q})}^2?$$ Answered by…

Question Number 181837 by mr W last updated on 01/Dec/22 $$findintegersa>b>c>0suchthat$$$$\frac{1}{a}+\frac{2}{b}+\frac{3}{c}=1$$ Commented by SEKRET last updated on 01/Dec/22 $$(2;5;30)(2;6;18)(2;7;14)(2;8;12)$$$$\left(\mathrm{2};\mathrm{10};\mathrm{10}\right)\:\left(\mathrm{2};\mathrm{12};\mathrm{9}\right)\left(\mathrm{2};\mathrm{16};\mathrm{8}\right)\left(\mathrm{2};\mathrm{28};\mathrm{7}\right)…

Question Number 181832 by henderson last updated on 01/Dec/22 $$\mathrm{help}!$$$$\int \frac{ln(x+1)}{x^2+1}dx=???$$ Commented by CElcedricjunior last updated on 01/Dec/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\boldsymbol{{x}}+\mathrm{1}\right)}{\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 50747 by behi83417@gmail.com last updated on 19/Dec/18 $${\mathit{x}}^2-{\mathit{y}}^2=\mathit{a},a\ne 0$$$${\mathit{y}}^2-{\mathit{z}}^2=\mathit{b},b\ne 0$$$${\mathit{z}}^2-{\mathit{x}}^2=\mathit{c},c\ne 0$$$$solvefor:x,y,z.$$ Commented…

Question Number 50730 by ajfour last updated on 19/Dec/18 $$\sqrt{x-a}+\sqrt{x-b}+\sqrt{x-c}+x=d$$$$solveforx.$$ Answered by behi83417@gmail.com last updated on 21/Dec/18 $$aftersquaringandsymplifingigot$$$${this}\:{equtition}: \…