Question Number 150960 by john_santu last updated on 17/Aug/21 $$\mathrm{given}\:\mathrm{x}\:,\mathrm{y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\: \\ $$$$\mathrm{with}\:\mathrm{x}<\mathrm{y}\:\mathrm{and}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{20l8}\:=\mathrm{30y}^{\mathrm{2}} −\mathrm{300y}+\mathrm{30l8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by otchereabdullai@gmail.com last updated on…
Question Number 85412 by Power last updated on 21/Mar/20 Commented by jagoll last updated on 22/Mar/20 $$\mathrm{by}\:\mathrm{observe} \\ $$$$\mathrm{x}\:=\:\mathrm{y} \\ $$$$\left(\mathrm{2x}\right)^{\mathrm{3}} \:=\:\mathrm{3}^{\mathrm{3}} \:\Rightarrow\:\mathrm{y}\:=\:\mathrm{x}=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left(\mathrm{2x}\right)^{\mathrm{2}}…
Question Number 85418 by oustmuchiya@gmail.com last updated on 21/Mar/20 $${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$ Commented by jagoll last updated on 22/Mar/20 $$\mathrm{let}\:\mathrm{2x}=\:\mathrm{u} \\ $$$$\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{u}}\right)^{\mathrm{3}} =\:\mathrm{u}^{\mathrm{3}} −\mathrm{3}\left(\mathrm{u}^{\mathrm{2}} \right)\left(\frac{\mathrm{1}}{\mathrm{u}}\right)+\mathrm{3u}\left(\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{2}}…
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Question Number 19875 by ajfour last updated on 16/Aug/17 Commented by ajfour last updated on 17/Aug/17 $${Find}\:{z}_{\mathrm{0}} \:,\:\frac{{p}}{{p}+{q}}\:,\:\frac{{r}}{{r}+{s}}\:;\:{in}\:{terms}\:{of} \\ $$$$\:\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} ,\:{and}\:{z}_{\mathrm{4}} \:. \\…
Question Number 150918 by mathdanisur last updated on 16/Aug/21 Commented by puissant last updated on 16/Aug/21 $$=\:\left[\frac{\underset{{k}=\mathrm{0}} {\overset{\mathrm{1995}} {\sum}}\mathrm{2}^{{k}} }{\mathrm{1997}}\right]\: \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{1997}}\left(\frac{\mathrm{1}−\mathrm{2}^{\mathrm{1996}} }{\mathrm{1}−\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{1997}}\left(\mathrm{2}^{\mathrm{1996}}…
Question Number 85365 by Power last updated on 21/Mar/20 Answered by jagoll last updated on 21/Mar/20 $$\mathrm{C}\:=\:\mathrm{S}_{\mathrm{112}} \:=\:\frac{\mathrm{112}}{\mathrm{2}}\left(−\mathrm{4}+\left(\mathrm{111}×\left(−\mathrm{8}\right)\right)\right. \\ $$$$=\:\mathrm{56}\:×\left(−\mathrm{892}\right) \\ $$$$=\:−\mathrm{49952} \\ $$ Commented…
Question Number 85358 by jagoll last updated on 21/Mar/20 $$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}\:}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{12} \\ $$ Answered by john santu last updated on 21/Mar/20 $${x}\:=\:{t}^{\mathrm{6}} \\ $$$$\Rightarrow\:{t}^{\mathrm{2}} +{t}^{\mathrm{3}} −\mathrm{12}=\mathrm{0}…
Question Number 150889 by mathdanisur last updated on 16/Aug/21 Answered by dumitrel last updated on 16/Aug/21 $$\Leftrightarrow{a}^{\mathrm{2}} +{a}\left({b}+{c}+{d}\right)+\left({b}+{c}+{d}\right)^{\mathrm{2}} \geqslant\mathrm{0}\Leftrightarrow \\ $$$$\left(\frac{{a}}{\mathrm{2}}+{b}+{c}+{d}\right)^{\mathrm{2}} +\frac{\mathrm{3}{a}^{\mathrm{2}} }{\mathrm{4}}\geqslant\mathrm{0} \\ $$$$,,=''\:{for}\:{a}=\mathrm{0};\:{b}+{c}+{d}=\mathrm{0}…
Question Number 150884 by mathdanisur last updated on 16/Aug/21 Answered by Rasheed.Sindhi last updated on 16/Aug/21 $$\overline {\mathrm{abcdef}}=?;\left\{\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\right\}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\} \\ $$$$\mathrm{6}\overline {\mid\mathrm{abcdef}},\mathrm{5}\mid\overline {\mathrm{abcde}},\mathrm{4}\mid\overline {\mathrm{abcd}},\mathrm{3}\mid\overline {\mathrm{abc}},\mathrm{2}\mid\overline {\mathrm{ab}}…