Question Number 28363 by abdo imad last updated on 24/Jan/18 $${simlify}\:{the}\:{sum}\:\:\:{S}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{{x}+\:{e}^{{i}\mathrm{2}{k}\pi} }{{x}\:−{e}^{{i}\mathrm{2}{k}\pi} }\:\:. \\ $$ Answered by ajfour last updated on 24/Jan/18 $${S}=\frac{{n}\left({x}+\mathrm{1}\right)}{{x}−\mathrm{1}}\:.…
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Question Number 159421 by HongKing last updated on 16/Nov/21 Commented by mr W last updated on 17/Nov/21 $${the}\:{next}\:{chance}\:{is}\:{three}\:{days}\:{later}… \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 159396 by quvonnn last updated on 16/Nov/21 Answered by som(math1967) last updated on 16/Nov/21 $${area}\:{of}\:\bigtriangleup{BCE}={Area}\:{of}\:\bigtriangleup{ECF} \\ $$$$\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4}×\mathrm{3}=\mathrm{6}\:{sq}.{unit} \\ $$$${CM}\:{is}\:{bisector}\:{of}\:\angle{C} \\ $$$$\:\therefore\frac{{EM}}{{MB}}\:=\frac{{EC}}{{CB}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{{Ar}\bigtriangleup{EMC}}{{Ar}\:\bigtriangleup{CMB}}=\frac{\mathrm{3}}{\mathrm{4}}…
Question Number 28327 by Rasheed.Sindhi last updated on 24/Jan/18 $$\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…
Question Number 28320 by NECx last updated on 24/Jan/18 $${If}\:{the}\:{arithmetic}\:{mean}\:{of}\:{a}\:{and} \\ $$$${b}\:{is}\:\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{\mathrm{2}},\:{show}\:{that}\:{n}=\mathrm{0} \\ $$ Commented by mrW2 last updated on 24/Jan/18 $${this}\:{is}\:{not}\:{always}\:{true},\:{sir}. \\…
Question Number 159394 by azadsir last updated on 16/Nov/21 $$\mathrm{if}\:\mathrm{a}^{\mathrm{3}} −\mathrm{b}^{\mathrm{3}} =\mathrm{513},\:\mathrm{ab}=\mathrm{54} \\ $$$$\:\mathrm{than},\:\mathrm{a}−\mathrm{b}\:=\:? \\ $$ Commented by cortano last updated on 16/Nov/21 $${a}^{\mathrm{3}} −{b}^{\mathrm{3}}…
Question Number 28319 by NECx last updated on 24/Jan/18 $${If}\:{the}\:{roots}\:{of}\:{x}^{\mathrm{2}} +{px}+{q}=\mathrm{0},\:{q}\neq\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta.{Find}\:{the}\:{roots}\:{of} \\ $$$${qx}^{\mathrm{2}} +\left(\mathrm{2}{q}−{p}^{\mathrm{2}} \right){x}+{q}=\mathrm{0}\:{in}\:{terms}\:{of} \\ $$$$\alpha\:{and}\:\beta. \\ $$ Answered by Rasheed.Sindhi last…
Question Number 159390 by pete last updated on 16/Nov/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:{x}\:\mathrm{and}\:{y}\:\mathrm{if} \\ $$$$\mathrm{log}_{\mathrm{4}} {x}\:+\mathrm{3}=\mathrm{log}_{\mathrm{27}} {y} \\ $$ Answered by abdullah_ff last updated on 16/Nov/21 $$\mathrm{log}_{\mathrm{4}} {x}+\mathrm{3}=\mathrm{log}_{\mathrm{27}}…