Category: Algebra

Question Number 186540 by akuba last updated on 05/Feb/23 $$ComplexNumbers$$$$Provethat$$$$1.\mid Z_1+Z_2\mid \le \mid Z_1\mid +\mid Z_2\mid$$$$\mathrm{2}.\:\mid{Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \mid\geq\mid{Z}_{\mathrm{1}} \mid−\mid{Z}_{\mathrm{2}} \mid \…

Question Number 120984 by pooooop last updated on 04/Nov/20 $$\frac{1}{1\cdot 4\cdot 7}+\frac{1}{4\cdot 7\cdot 10}+\frac{1}{7\cdot 10\cdot 13}+\dots +\frac{1}{25\cdot 28\cdot 31}=?$$ Answered by Dwaipayan Shikari last updated on 04/Nov/20 $$T_n=\frac{1}{(3n-2)(3n+1)(3n+4)}$$$$\overset{{n}} {\sum}{T}_{{n}}…

Question Number 120960 by Jamshidbek2311 last updated on 04/Nov/20 $$Ifx,y,z>0thenprovefollowing$$$$inequality$$$$(x^2+2)(y^2+2)(z^2+2)⩾9(xy+yz+xz)$$ Terms of Service Privacy Policy Contact:…

Question Number 120953 by bemath last updated on 04/Nov/20 $$\mathrm{solve}\mathrm{in}\mathrm{x}\in \mathbb{R}$$$$\mid 3\mathrm{x}-4\mid =\mathrm{x}-5$$ Answered by TANMAY PANACEA last updated on 04/Nov/20 $$when(3x-4)>0\to x>\frac{4}{3}$$$$\left(\mathrm{3}{x}−\mathrm{4}\right)={x}−\mathrm{5}…

Question Number 55415 by Tawa1 last updated on 23/Feb/19 $$\mathrm{a},\mathrm{b},\mathrm{d}\mathrm{are}\mathrm{gp}.\mathrm{such}\mathrm{that}\mathrm{a},\mathrm{b},\mathrm{c}\mathrm{are}\mathrm{real}.\mathrm{if}$$$$\mathrm{a}+\mathrm{b}+\mathrm{c}=26\mathrm{and}{\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2=364,\mathrm{find}\mathrm{b}?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Feb/19 $${a}={a}…