Question Number 9874 by j.masanja06@gmail.com last updated on 11/Jan/17 $$\mathrm{if}\:\mathrm{the}\:\mathrm{eqution}\:\mathrm{x}^{\mathrm{3}} +\mathrm{3hx}\:+\:\mathrm{q}=\mathrm{0}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\alpha,\beta\:\:\mathrm{and}\:\gamma. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{eqution}\:\mathrm{with}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}; \\ $$$$\left(\mathrm{i}\right)\frac{\mathrm{1}}{\alpha\beta}\:+\:\frac{\mathrm{1}}{\beta\gamma}\:+\:\frac{\mathrm{1}}{\alpha\gamma} \\ $$$$\left(\mathrm{ii}\right)\frac{\mathrm{1}}{\alpha^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\beta^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\gamma^{\mathrm{2}} } \\ $$$$ \\…
Question Number 9869 by bansal22luvi@gmail.com last updated on 10/Jan/17 $${find}\:{the}\:{value}\:{of} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\:\:\frac{{n}}{\mathrm{1}+{n}^{\mathrm{2}} +{n}^{\mathrm{4}} } \\ $$$$\left.{a}\right)\mathrm{0}.\mathrm{46}\:{and}\:\mathrm{0}.\mathrm{47} \\ $$$$\left.{b}\right)\mathrm{0}.\mathrm{47}\:{and}\:\mathrm{0}.\mathrm{48} \\ $$$$\left.{c}\right)\mathrm{0}.\mathrm{48}\:{and}\:\mathrm{0}.\mathrm{49} \\ $$$$\left.{d}\right)\mathrm{0}.\mathrm{49}\:{and}\:\mathrm{0}.\mathrm{50} \\…
Question Number 140939 by iloveisrael last updated on 14/May/21 $$\:{x}^{\mathrm{sgn}\:\left({x}^{\mathrm{3}} −{x}\right)} \:=\:{x}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}\: \\ $$ Answered by john_santu last updated on 14/May/21 $$\:{x}\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\:\wedge\:{x}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$…
Question Number 140915 by mathdanisur last updated on 14/May/21 Commented by mr W last updated on 14/May/21 $${question}\:{is}\:{wrong}! \\ $$$$\mathrm{12}+\mathrm{18}+\mathrm{144}+\mathrm{12}=\mathrm{186}>\mathrm{180}! \\ $$ Commented by mathdanisur…
Question Number 140908 by ajfour last updated on 14/May/21 $$\:\:{ab}={c} \\ $$$${let}\:\:\:\left({a}−{p}\right)\left({b}−{q}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:{c}−\left({aq}+{bp}\right)+{pq}=\mathrm{0} \\ $$$${q}=\frac{{bp}−{c}}{{p}−{a}} \\ $$$${say}\:\:\:\mathrm{4}×\mathrm{2}=\mathrm{8} \\ $$$$\:\:\:\:\:\left(\mathrm{4}−\mathrm{3}\right)\left(\mathrm{2}−\frac{\mathrm{6}−\mathrm{8}}{−\mathrm{1}}\right)=\mathrm{1}×\mathrm{0}=\mathrm{0} \\ $$$${And}\:\:{if}\:\:{q}={b} \\ $$$$\:\:{p}=\frac{{ab}−{c}}{\mathrm{2}{b}}=\mathrm{0} \\…
Question Number 75368 by vishalbhardwaj last updated on 10/Dec/19 $$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:{f}\left({x}\right)\:=\:{sinx}\:+\:{cosx},\:\mathrm{for}\:\:{x}\in\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{is}\:\mathrm{strictly}\:\mathrm{inceasing}\:\mathrm{and}\:\mathrm{srictly}\:\mathrm{decreasing}\:? \\ $$ Commented by vishalbhardwaj last updated on 10/Dec/19…
Question Number 140900 by bramlexs22 last updated on 14/May/21 $$\:\begin{cases}{\mathrm{x}^{\mathrm{3}} =\mathrm{xyz}+\mathrm{1}}\\{\mathrm{y}^{\mathrm{3}} =\mathrm{xyz}+\mathrm{2}}\\{\mathrm{z}^{\mathrm{3}} =\mathrm{xyz}−\mathrm{3}}\end{cases} \\ $$ Commented by bramlexs22 last updated on 14/May/21 $$\mathrm{Thank}\:\mathrm{all}\:\mathrm{master} \\ $$…
Question Number 9827 by tawakalitu last updated on 06/Jan/17 $$\left(\mathrm{7}\:−\:\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}} \:+\:\left(\mathrm{7}\:+\:\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}} \:=\:\mathrm{14} \\ $$ Answered by ridwan balatif last updated on 06/Jan/17 $$\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}=\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)\frac{\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)}{\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)}…
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Question Number 140899 by ajfour last updated on 14/May/21 Commented by ajfour last updated on 14/May/21 Commented by ajfour last updated on 14/May/21 $${construction}\:{method}\:{please}.. \\…