Question Number 137588 by bramlexs22 last updated on 04/Apr/21 $${For}\:{a}\:{positive}\:{number}\:{n}\:,\:{let} \\ $$$${f}\left({n}\right)\:{be}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({n}\right)=\frac{\mathrm{4}{n}+\sqrt{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}}{\:\sqrt{\mathrm{2}{n}+\mathrm{1}}\:+\sqrt{\mathrm{2}{n}−\mathrm{1}}} \\ $$$${calculate}\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+…+{f}\left(\mathrm{40}\right). \\ $$ Answered by bemath last updated on…
Question Number 6512 by Rasheed Soomro last updated on 30/Jun/16 $${Find}\:{complex}\:{number}\:{whose}\:{additive}\: \\ $$$${inverse}\:{is}\:{equal}\:{to}\:{its}\:{multiplicative} \\ $$$${inverse}. \\ $$ Commented by Temp last updated on 30/Jun/16 $$\mathrm{What}\:\mathrm{is}\:\mathrm{additive}\:\mathrm{and}\:\mathrm{multiplicitive}…
Question Number 137584 by bramlexs22 last updated on 04/Apr/21 $${Given}\:\begin{cases}{{a}_{\mathrm{2}{n}} \:=\:{a}_{{n}} .{a}_{\mathrm{2}} \:+\mathrm{1}}\\{{a}_{\mathrm{2}{n}+\mathrm{1}} \:=\:{a}_{{n}} .{a}_{\mathrm{2}} \:−\mathrm{2}\:}\end{cases}\:{and} \\ $$$$\:\begin{cases}{{a}_{\mathrm{7}} \:=\:\mathrm{2}}\\{\mathrm{0}<{a}_{\mathrm{1}} <\mathrm{1}}\end{cases}.\:{Find}\:{a}_{\mathrm{25}} \:=? \\ $$$$ \\ $$…
Question Number 137568 by JulioCesar last updated on 04/Apr/21 Commented by JulioCesar last updated on 04/Apr/21 $${why}\:{it}\:{has}\:{background}?? \\ $$ Commented by mr W last updated…
Question Number 137563 by liberty last updated on 04/Apr/21 $${let}\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }={k} \\ $$$${find}\:{the}\:{value}\:{of}\:\frac{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }+\frac{{x}^{\mathrm{8}} −{y}^{\mathrm{8}}…
Question Number 6483 by sanusihammed last updated on 28/Jun/16 $$\mathrm{5}^{\sqrt{{x}\:}} \:\:−\:\:\:\mathrm{5}^{\left({x}\:−\:\mathrm{7}\right)} \:\:=\:\:\mathrm{100} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x} \\ $$ Answered by Yozzii last updated on 29/Jun/16…
Question Number 6476 by sanusihammed last updated on 28/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $${Given}\:{equation}:\:{x}^{\mathrm{2}} −{px}+\mathrm{8}=\mathrm{0} \\ $$$$\:\:\:\:\:{Sum}\:{of}\:{the}\:{roots}\:=−\frac{{coefficient}\:{of}\:{x}}{{coefficient}\:{of}\:{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=−\frac{−{p}}{\mathrm{1}}={p} \\…
Question Number 6436 by sanusihammed last updated on 27/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $${P}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +{ax}+{b} \\ $$$${x}−\mathrm{2}\:{is}\:{factor}\:{of}\:{P}\left({x}\right)\:{means}\:{if}\:{P}\left({x}\right)\:{is}\:{divided} \\ $$$${by}\:{x}−\mathrm{2}\:,\:{the}\:{remainder}\:{will}\:{be}\:\mathrm{0} \\…
Question Number 71960 by TawaTawa last updated on 22/Oct/19 Answered by mind is power last updated on 22/Oct/19 $$\Sigma\frac{\mathrm{1}+\mathrm{a}}{\mathrm{1}−\mathrm{a}}=\Sigma\left(−\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}}\right)=\Sigma−\mathrm{1}+\Sigma\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}} \\ $$$$\frac{\mathrm{p}'\left(\mathrm{x}\right)}{\mathrm{p}\left(\mathrm{x}\right)}=\underset{\mathrm{a}\in\mathrm{Root}\left(\mathrm{p}\right)} {\sum}\frac{\mathrm{1}}{\mathrm{x}−\mathrm{a}} \\ $$$$\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{3}}…
Question Number 71946 by oyemi kemewari last updated on 22/Oct/19 Answered by MJS last updated on 23/Oct/19 $$\mathrm{12}=\mathrm{3}{y}\left(\frac{\mathrm{3}{y}}{\mathrm{3}+\mathrm{3}{y}}\right)^{\mathrm{2}/\mathrm{3}} \left(\frac{\mathrm{1}}{\mathrm{400}}\right)^{\mathrm{1}/\mathrm{2}} \\ $$$$\mathrm{80}={y}\left(\frac{{y}}{{y}+\mathrm{1}}\right)^{\mathrm{2}/\mathrm{3}} \\ $$$$\mathrm{512000}={y}^{\mathrm{3}} \frac{{y}^{\mathrm{2}} }{\left({y}+\mathrm{1}\right)^{\mathrm{2}}…