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Category: Algebra

a-b-10-i-ab-c-0-ii-ac-d-6-iii-ad-1-iv-a-b-c-d-Note-This-problem-is-related-to-solve-the-equation-t-4-10t-6t-1-0-of-Q-35844-

Question Number 36132 by Rasheed.Sindhi last updated on 29/May/18 $${a}+{b}=\mathrm{10}………\left(\mathrm{i}\right) \\ $$$${ab}+{c}=\mathrm{0}……….\left(\mathrm{ii}\right) \\ $$$${ac}+{d}=\mathrm{6}……….\left(\mathrm{iii}\right) \\ $$$${ad}=−\mathrm{1}………..\left(\mathrm{iv}\right) \\ $$$$\left({a},{b},{c},{d}\right)=? \\ $$$$\mathcal{N}{ote}:\:{This}\:{problem}\:{is}\:{related}\:{to}\:{solve} \\ $$$${the}\:{equation}\:\left({t}^{\mathrm{4}} +\mathrm{10}{t}+\mathrm{6}{t}−\mathrm{1}=\mathrm{0}\right)\:{of} \\ $$$${Q}#\mathrm{35844}…

x-4-10x-3-6x-1-x-2-5-1-2-x-2-10x-5-1-2-

Question Number 36126 by Rasheed.Sindhi last updated on 29/May/18 $$\mathrm{x}^{\mathrm{4}} +\mathrm{10x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\overset{?} {=}\left({x}^{\mathrm{2}} +\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)\left({x}^{\mathrm{2}} +\mathrm{10}{x}−\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}\right) \\ $$ Commented by Rasheed.Sindhi last updated on…

Question-If-a-Z-and-the-function-with-the-following-rule-is-differentiable-at-x-1-then-find-the-value-of-a-f-x-

Question Number 167196 by mnjuly1970 last updated on 09/Mar/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:#\:{Question}\:# \\ $$$$\:\:\:\:\:{If}\:,\:{a}\:\notin\:\mathbb{Z}\:\:{and}\:\:{the}\:{function}\:{with}\:{the}\:\:{following}\:\:{rule}\:\: \\ $$$$\:\:\:\:\:\:{is}\:\:{differentiable}\:{at}\:\:\:\:''\:\:{x}\:=\:\mathrm{1}\:''\:\:{then}\:\:{find}\:\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:\:“\:\:\:{a}\:\:“\:\:\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)\:=\:\left(\lfloor\:\frac{{x}}{\mathrm{2}}\:\rfloor\:+\:\lfloor\:\frac{−{x}}{\mathrm{2}}\:\rfloor\:\right)\mid\:{x}^{\:\mathrm{2}} +{x}\:−\mathrm{2}\mid\:\lfloor{ax}\:\rfloor\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$ \\ $$…

Find-the-equation-of-the-locus-of-a-moving-point-P-such-that-its-distance-from-the-point-A-4-3-and-B-5-1-is-in-the-ratio-3-1-

Question Number 167185 by pete last updated on 09/Mar/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{moving}\:\mathrm{point}\:\mathrm{P}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point} \\ $$$$\mathrm{A}\left(\mathrm{4},\mathrm{3}\right)\:\mathrm{and}\:\mathrm{B}\left(\mathrm{5},\mathrm{1}\right)\:\mathrm{is}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}\::\:\mathrm{1} \\ $$ Commented by mr W last updated on 09/Mar/22 $${the}\:{locus}\:{of}\:{a}\:{moving}\:{point},\:{whose}…

Question-167165

Question Number 167165 by mathlove last updated on 08/Mar/22 Answered by MJS_new last updated on 08/Mar/22 $$\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:{x},\:{y}\:\in\mathbb{Z} \\ $$$$\mathrm{1}\:\mathrm{solution}\:\mathrm{for}\:{x},\:{y}\:\in\mathbb{Q} \\ $$$$\mathrm{4}\:\mathrm{solutions}\:\mathrm{for}\:{x},\:{y}\:\in\mathbb{R} \\ $$ Terms of…

Question-167137

Question Number 167137 by mr W last updated on 07/Mar/22 Answered by som(math1967) last updated on 07/Mar/22 $$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\:+\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{{a}+{b}+{c}}\:\:\left[\because\:{a}+{b}+{c}=\mathrm{2022}\right] \\ $$$$\left({a}+{b}+{c}\right)\left({ab}+{bc}+{ca}\right)−{abc}=\mathrm{0} \\ $$$$\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)=\mathrm{0} \\ $$$${if}\:{a}+{b}=\mathrm{0} \\…