Question Number 48193 by peter frank last updated on 20/Nov/18 $${In}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${one}\:{root}\:{is}\:{square}\:{of}\: \\ $$$${orther}.{without}\:{solving} \\ $$$${the}\:{equation}.{prove}\:{that} \\ $$$${c}\left({a}−{b}\right)^{\mathrm{3}} ={a}\left({c}−{b}\right)^{\mathrm{3}} \\ $$ Answered by…
Question Number 113689 by Ar Brandon last updated on 14/Sep/20 $$\mathrm{Find}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} =\mathrm{101}^{\mathrm{2}} .\:\mathrm{Where}\:\mathrm{p},\:\mathrm{q}\in\mathbb{Z}\: \\ $$$$\mathrm{different}\:\mathrm{from}\:\mathrm{zero}. \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 48091 by peter frank last updated on 19/Nov/18 Commented by maxmathsup by imad last updated on 19/Nov/18 $${we}\:{have}\:{e}^{−{x}} {sinx}\:={Im}\left({e}^{−{x}+{ix}} \right)={Im}\left({e}^{\left(−\mathrm{1}+{i}\right){x}} \right)\:{but} \\ $$$${e}^{\left(−\mathrm{1}+\boldsymbol{{i}}\right)\boldsymbol{{x}}}…
Question Number 48090 by peter frank last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\left.\mathrm{1}\right){true}\:{value}\:{of}\:{product}\:{of}\:{length}×{width} \\ $$$$=\mathrm{2}.\mathrm{29}×\mathrm{1}.\mathrm{29}=\left(\mathrm{2}.\mathrm{30}−\mathrm{0}.\mathrm{01}\right)\left(\mathrm{1}.\mathrm{30}−\mathrm{0}.\mathrm{01}\right) \\ $$$$=\mathrm{2}.\mathrm{30}×\mathrm{1}.\mathrm{30}−\mathrm{0}.\mathrm{01}\left(\mathrm{2}.\mathrm{30}+\mathrm{1}.\mathrm{30}\right)+\mathrm{0}.\mathrm{0001} \\ $$$$=\mathrm{2}.\mathrm{30}×\mathrm{1}.\mathrm{30}−\mathrm{3}.\mathrm{60}×\mathrm{0}.\mathrm{01}+\mathrm{0}.\mathrm{0001} \\…
Question Number 113593 by bemath last updated on 14/Sep/20 $$\frac{\mathrm{6}}{\mathrm{5}×\mathrm{14}}+\frac{\mathrm{6}}{\mathrm{14}×\mathrm{23}}+\frac{\mathrm{6}}{\mathrm{23}×\mathrm{32}}+…+\frac{\mathrm{6}}{\left(\mathrm{9}{n}−\mathrm{4}\right)\left(\mathrm{9}{n}+\mathrm{5}\right)}=? \\ $$ Commented by bemath last updated on 14/Sep/20 $${thank}\:{you}\:{both}\:{sir} \\ $$ Answered by bobhans…
Question Number 47976 by peter frank last updated on 17/Nov/18 Commented by maxmathsup by imad last updated on 17/Nov/18 $${let}\:{A}\:=\int_{\frac{\mathrm{1}}{\mathrm{4}}} ^{\frac{\mathrm{3}}{\mathrm{4}}} \:\:\:\frac{\left(\sqrt{{x}−{x}^{\mathrm{2}} }\right)^{−\mathrm{1}} }{\left({dx}\right)^{−\mathrm{2}} }\:\left({dx}\right)^{−\mathrm{1}}…
Question Number 178992 by Spillover last updated on 23/Oct/22 Answered by som(math1967) last updated on 23/Oct/22 $$\theta_{\mathrm{2}} −\theta_{\mathrm{1}} =\theta_{\mathrm{3}} −\theta_{\mathrm{2}} =…=\theta_{{n}} −\theta_{{n}−\mathrm{1}} ={d} \\ $$$${sec}\theta_{\mathrm{1}}…
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Question Number 178994 by Spillover last updated on 23/Oct/22 Commented by Spillover last updated on 23/Oct/22 Answered by mr W last updated on 23/Oct/22 $${say}\:{the}\:{digits}\:{are}\:{a},{b},{c}\:{from}\:{left}\:{to}…
Question Number 178969 by Tawa11 last updated on 23/Oct/22 "How many integers between 100 – 999 inclusive consist of distinct odd digit" Answered by Rasheed.Sindhi…