Category: Algebra

Question Number 213621 by hardmath last updated on 10/Nov/24 $$\mathrm{a},\mathrm{b}>0$$$$\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}=2\mathrm{and}{\mathrm{a}}^2+{\mathrm{b}}^2=12$$$$\mathrm{a}+\mathrm{b}=?$$ Answered by Ghisom last updated on 10/Nov/24…

Question Number 213535 by justenspi last updated on 07/Nov/24 $$\mathrm{Are}\mathrm{not}\mathrm{there}\mathrm{simple}\mathrm{means}\mathrm{of}\mathrm{solving}\mathrm{this}$$$$\mathrm{system}\mathrm{of}\mathrm{equations}\mathrm{in}\mathrm{non}-\mathrm{negative}\mathrm{reals}$$ Commented by justenspi last updated on 07/Nov/24 Terms of Service Privacy…

Question Number 213467 by efronzo1 last updated on 06/Nov/24 $$\underbrace{\mathit{B}}$$ Commented by mr W last updated on 06/Nov/24 �� Commented by mr W…

Question Number 213459 by golsendro last updated on 06/Nov/24 $$\mathrm{Find}\mathrm{tupple}\mathrm{natural}\mathrm{numbers}(\mathrm{a},\mathrm{b},\mathrm{c})$$$$\mathrm{such}\mathrm{that}$$$$\{\begin{array}{l}\max \{\frac{\mathrm{a}+\mathrm{b}}{2}+\frac{\mid \mathrm{a}-\mathrm{b}\mid }{2},\frac{\mathrm{b}+\mathrm{c}}{2}+\frac{\mid \mathrm{b}-\mathrm{c}\mid }{2},\frac{\mathrm{c}+\mathrm{a}}{2}+\frac{\mid \mathrm{c}-\mathrm{a}\mid }{2}\}=\mathrm{a}\\ \min \{\frac{\mathrm{a}+\mathrm{b}}{2}-\frac{\mid \mathrm{a}-\mathrm{b}\mid }{2},\frac{\mathrm{b}+\mathrm{c}}{2}-\frac{\mid \mathrm{b}-\mathrm{c}\mid }{2},\frac{\mathrm{c}+\mathrm{a}}{2}-\frac{\mid \mathrm{c}-\mathrm{a}\mid }{2}\}=\mathrm{b}\end{array}$$$$\mathrm{where}\mathrm{a}+\mathrm{b}+\mathrm{c}=10$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 213482 by efronzo1 last updated on 06/Nov/24 Answered by A5T last updated on 06/Nov/24 $$3\mid Y\Rightarrow 8+c+2+3+d\equiv 0\left(mod3\right)\Rightarrow c+d\equiv 2\left(mod3\right)$$$$3\mid X\Rightarrow 9\mid Y:$$$$3+1+a+5+b\equiv 0\left(mod3\right)\Rightarrow 8+c+2+3+d\equiv 0\left(mod9\right)$$$$\Rightarrow a+b\equiv 0\left(mod3\right)\Rightarrow c+d\equiv 5\left(mod9\right)$$$$\mathrm{3}\mid{X}\Rightarrow{c}+{d}=\mathrm{5}\Rightarrow{a}+{b}=\mathrm{0},\mathrm{3},\mathrm{6},\mathrm{9}\:\wedge\:{c}+{d}=\mathrm{5}…