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Category: Algebra

Question-128918

Question Number 128918 by Koyoooo last updated on 11/Jan/21 Commented by MJS_new last updated on 11/Jan/21 $$\mathrm{not}\:\mathrm{true}. \\ $$$$\mathrm{i}.\mathrm{e}.\:{a}=\mathrm{0}\wedge{b}=−\mathrm{4}\:\Rightarrow\:\mathrm{result}\:\mathrm{is}\:\mathrm{32} \\ $$ Commented by mr W…

solve-for-both-x-and-n-in-equation-x-n-216-in-all-part-of-integer-A-n-3-x-6-B-n-4-x-5-C-n-5-x-4-D-n-6-x-3-

Question Number 63381 by minh2001 last updated on 03/Jul/19 $${solve}\:{for}\:{both}\:{x}\:{and}\:{n} \\ $$$${in}\:{equation}:\:{x}^{{n}} =\mathrm{216}\:{in}\:{all} \\ $$$${part}\:{of}\:{integer} \\ $$$$\mathscr{A}\:\underset{{n}=\mathrm{3}} {\overset{{x}=\mathrm{6}} {\left\{}}\right. \\ $$$$\mathscr{B}\underset{{n}=\mathrm{4}} {\overset{{x}=\mathrm{5}} {\left\{}}\right. \\ $$$$\mathscr{C}\underset{{n}=\mathrm{5}}…

solve-this-equation-in-all-part-of-complex-number-x-9-3x-2-1-x-6-4-x-9-3x-2-1-x-6-16-

Question Number 63383 by minh2001 last updated on 03/Jul/19 $${solve}\:{this}\:{equation}\:{in}\:{all}\: \\ $$$${part}\:{of}\:{complex}\:{number}: \\ $$$$\sqrt{\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)+\mathrm{4}}=\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)−\mathrm{16} \\ $$ Commented by MJS last updated…

just-found-this-on-the-web-I-thought-it-might-help-in-some-cases-where-quartics-appear-i-e-Sir-Aifour-s-geometric-questions-sometimes-we-know-the-nature-of-the-roots-but-how-to-use-this-information

Question Number 63373 by MJS last updated on 31/Jul/19 $$\mathrm{just}\:\mathrm{found}\:\mathrm{this}\:\mathrm{on}\:\mathrm{the}\:\mathrm{web} \\ $$$$\mathrm{I}\:\mathrm{thought}\:\mathrm{it}\:\mathrm{might}\:\mathrm{help}\:\mathrm{in}\:\mathrm{some}\:\mathrm{cases}\:\mathrm{where} \\ $$$$\mathrm{quartics}\:\mathrm{appear}\:\mathrm{i}.\mathrm{e}.\:\mathrm{Sir}\:\mathrm{Aifour}'\mathrm{s}\:\mathrm{geometric} \\ $$$$\mathrm{questions}.\:\mathrm{sometimes}\:\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{roots},\:\mathrm{but}\:\mathrm{how}\:\mathrm{to}\:\mathrm{use}\:\mathrm{this}\:\mathrm{information}? \\ $$$$ \\ $$$${ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e}=\mathrm{0}…

x-4x-16x-64x-4-2019-x-3-x-1-x-

Question Number 128850 by ruwedkabeh last updated on 10/Jan/21 $$\sqrt{{x}+\sqrt{\mathrm{4}{x}+\sqrt{\mathrm{16}{x}+\sqrt{\mathrm{64}{x}+…+\sqrt{\mathrm{4}^{\mathrm{2019}} {x}+\mathrm{3}}}}}}−\sqrt{{x}}=\mathrm{1} \\ $$$${x}=? \\ $$ Answered by mindispower last updated on 10/Jan/21 $$\Rightarrow\sqrt{\mathrm{4}{x}+……+\sqrt{\mathrm{4}^{\mathrm{2009}} {x}+\mathrm{3}}}=\mathrm{1}+\mathrm{2}\sqrt{{x}} \\…

find-some-of-all-real-x-such-that-4x-2-15x-17-x-2-4x-12-5x-2-16x-18-2x-2-5x-13-

Question Number 63291 by aliesam last updated on 02/Jul/19 $${find}\:{some}\:{of}\:{all}\:{real}\:{x}\:{such}\:{that} \\ $$$$ \\ $$$$\frac{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{15}{x}+\mathrm{17}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{12}}\:=\:\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{16}{x}+\mathrm{18}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{13}} \\ $$ Commented by Prithwish sen last…

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Question Number 63247 by Joel122 last updated on 01/Jul/19 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\sqrt{{abc}}\:+\:\sqrt{\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)}\:\leqslant\:\mathrm{1} \\ $$$$\mathrm{for}\:\mathrm{0}\:\leqslant\:{a},{b},{c}\:\leqslant\:\mathrm{1} \\ $$ Commented by Tony Lin last updated on 01/Jul/19 $$\because\:{abc}+\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)\geqslant…

fine-the-number-thats-divided-by-3-4-5-and-9-and-produce-the-remanider-with-order-1-3-5-and-7-

Question Number 128715 by Study last updated on 09/Jan/21 $${fine}\:{the}\:{number}\:{thats}\:{divided}\:{by}\: \\ $$$$\mathrm{3},\mathrm{4},\mathrm{5}\:{and}\:\mathrm{9}\:{and}\:{produce}\:{the}\:{remanider} \\ $$$${with}\:{order}\:\mathrm{1},\mathrm{3},\mathrm{5}\:{and}\:\mathrm{7}?? \\ $$ Commented by mr W last updated on 10/Jan/21 $${do}\:{you}\:{mean}:…