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Category: Algebra

let-give-F-x-1-x-2-1-prove-that-P-n-Z-n-x-F-n-x-P-n-x-1-x-2-n-find-a-relation-of-recurence-between-the-P-n-prove-that-all-roots-of-P-n-are-reals-and-smples-

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Question Number 28364 by abdo imad last updated on 24/Jan/18 $${let}\:{give}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{prove}\:{that}\:\exists\:{P}_{{n}} \in\:{Z}_{{n}} \left[{x}\right]\:/ \\ $$$${F}^{\left({n}\right)} \left({x}\right)=\:\:\frac{{P}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:\:{find}\:{a}\:{relation}\:{of}\:{recurence}\:{between}\: \\ $$$${the}\:\:{P}_{{n}} \:.{prove}\:{that}\:{all}\:{roots}\:{of}\:{P}_{{n}} \:{are}\:{reals}\:{and}\:{smples}. \\…

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Question-159396

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Question Number 159396 by quvonnn last updated on 16/Nov/21 Answered by som(math1967) last updated on 16/Nov/21 $${area}\:{of}\:\bigtriangleup{BCE}={Area}\:{of}\:\bigtriangleup{ECF} \\ $$$$\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4}×\mathrm{3}=\mathrm{6}\:{sq}.{unit} \\ $$$${CM}\:{is}\:{bisector}\:{of}\:\angle{C} \\ $$$$\:\therefore\frac{{EM}}{{MB}}\:=\frac{{EC}}{{CB}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{{Ar}\bigtriangleup{EMC}}{{Ar}\:\bigtriangleup{CMB}}=\frac{\mathrm{3}}{\mathrm{4}}…

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Given-that-a-n-1-b-n-1-a-n-b-n-is-AM-between-a-and-b-where-a-b-a-b-0-find-out-the-value-of-n-

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Question Number 28327 by Rasheed.Sindhi last updated on 24/Jan/18 $$\mathrm{Given}\:\mathrm{that}\:\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }\:\mathrm{is}\:\mathrm{AM}\:\mathrm{between}\:{a} \\ $$$$\mathrm{and}\:{b}\:,\mathrm{where}\:{a}\neq{b}\:\wedge\:{a},{b}\neq\mathrm{0};\:\mathrm{find}\:\mathrm{out}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}. \\ $$ Answered by mrW2 last updated on 24/Jan/18…

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