Menu Close

Category: Algebra

For-x-0-Z-prove-that-x-3-x-x-3-x-1-8-x-2-x-2-x-2-GIF-and-x-x-x-

Question Number 156642 by MathSh last updated on 13/Oct/21 $$\mathrm{For}\:\:\mathrm{x}\in\left(\mathrm{0};\infty\right)\:-\:\mathbb{Z}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\left\{\mathrm{x}\right\}^{\mathrm{3}} }{\left[\mathrm{x}\right]}\:+\:\frac{\left[\mathrm{x}\right]^{\mathrm{3}} }{\left\{\mathrm{x}\right\}}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{8}}\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\left[\mathrm{x}\right]^{\mathrm{2}} \:+\:\left\{\mathrm{x}\right\}^{\mathrm{2}} \right) \\ $$$$\left[\ast\right]-\mathrm{GIF}\:\:\mathrm{and}\:\:\left\{\mathrm{x}\right\}=\mathrm{x}-\left[\mathrm{x}\right] \\ $$ Commented by ghimisi last…

x-3-x-c-x-4-x-2-cx-let-cx-kx-4-hx-2-kx-3-hx-c-x-2-1-c-kx-2-h-x-2-1-ch-1-ck-1-ch-1-ck-k-1-ch-1-ck-h-2-c-2-1-ch-h-k-2-c-2-1-ck-3-1-ch-h-2-k-2-2hk-

Question Number 156639 by ajfour last updated on 13/Oct/21 $$\mathrm{x}^{\mathrm{3}} =\mathrm{x}+\mathrm{c} \\ $$$$\mathrm{x}^{\mathrm{4}} =\mathrm{x}^{\mathrm{2}} +\mathrm{cx} \\ $$$$\mathrm{let}\:\:\mathrm{cx}=\mathrm{kx}^{\mathrm{4}} +\mathrm{hx}^{\mathrm{2}} \\ $$$$\Rightarrow\:\:\mathrm{kx}^{\mathrm{3}} +\mathrm{hx}=\mathrm{c} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{1}+\mathrm{c}\left(\mathrm{kx}^{\mathrm{2}} +\mathrm{h}\right)…

If-x-2sec-3t-and-y-4tan-3t-Show-that-y-4-x-2-4-

Question Number 25536 by tawa tawa last updated on 11/Dec/17 $$\mathrm{If}\:\:\:\mathrm{x}\:=\:\mathrm{2sec}\left(\mathrm{3t}\right)\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{4tan}\left(\mathrm{3t}\right),\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\mathrm{y}\:=\:\mathrm{4}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right) \\ $$ Answered by prakash jain last updated on 11/Dec/17 $${x}=\mathrm{2sec}\:\mathrm{3}{t}\Rightarrow\frac{{x}}{\mathrm{2}}=\mathrm{sec}\:\mathrm{3}{t} \\ $$$${y}=\mathrm{4tan}\:\mathrm{3}{t}\Rightarrow\frac{{y}}{\mathrm{4}}=\mathrm{tan}\:\mathrm{3}{t}…

Three-sets-of-beans-l-m-and-n-are-sold-for5-for-5-00-15-00-and-17-50-respectively-per-kg-If-they-are-mixed-in-the-ratio-of-1-3-2-what-is-the-cost-per-kg-of-the-mixture-

Question Number 25533 by pieroo last updated on 11/Dec/17 $${Three}\:{sets}\:{of}\:{beans}\:{l},\:{m},\:{and}\:{n}\:{are}\:{sold}\:{for}\mathrm{5} \\ $$$${for}\:\$\mathrm{5}.\mathrm{00},\:\$\mathrm{15}.\mathrm{00}\:{and}\:\$\mathrm{17}.\mathrm{50}\:{respectively} \\ $$$${per}\:{kg}.\:{If}\:{they}\:{are}\:{mixed}\:{in}\:{the}\:{ratio}\:{of} \\ $$$$\mathrm{1}:\mathrm{3}:\mathrm{2},\:{what}\:{is}\:{the}\:{cost}\:{per}\:{kg}\:{of}\:{the}\:{mixture}?× \\ $$ Answered by mrW1 last updated on 11/Dec/17…

Find-all-the-triplets-a-b-c-of-pozitif-integers-such-that-a-3-b-3-c-3-abc-2-

Question Number 156591 by amin96 last updated on 12/Oct/21 $${Find}\:{all}\:{the}\:{triplets}\:\left({a},\:{b},\:{c}\right)\:{of}\:{pozitif}\:{integers} \\ $$$${such}\:{that} \\ $$$$\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\boldsymbol{\mathrm{c}}^{\mathrm{3}} =\left(\boldsymbol{\mathrm{abc}}\right)^{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$$$?????? \\ $$…