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Category: Algebra

f-0-1-R-f-x-4-x-2-4-x-is-given-find-the-value-of-the-following-expression-E-f-1-20-f-2-20-

Question Number 185983 by mnjuly1970 last updated on 30/Jan/23 $$ \\ $$$$\:\:\:\:\:\begin{cases}{\:\:\:{f}\::\:\:\left[\:\:\mathrm{0}\:\:,\:\:\mathrm{1}\:\right]\:\rightarrow\:\mathbb{R}}\\{\:\:\:\:{f}\:\left({x}\:\right)\:=\:\frac{\:\mathrm{4}^{\:{x}} }{\mathrm{2}\:+\:\mathrm{4}^{\:{x}} }}\end{cases} \\ $$$$\:\:\:\:\:\:{is}\:\:{given}\:.\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:{the}\:{following}\:{expression}. \\ $$$$\:\:\:\:\:\:\mathrm{E}\:=\:{f}\:\left(\frac{\mathrm{1}}{\mathrm{20}}\:\right)+\:{f}\left(\frac{\:\mathrm{2}}{\mathrm{20}}\:\right)+…\:+{f}\:\left(\frac{\mathrm{19}}{\mathrm{20}}\right)\:−{f}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right)=? \\ $$ Answered by ARUNG_Brandon_MBU…

solve-in-R-2x-3x-1-x-greatest-integer-number-more-than-or-equal-to-x-

Question Number 185981 by mnjuly1970 last updated on 30/Jan/23 $$ \\ $$$$\:\:\:\:\:\:\:{solve}\:\:{in}\:\:\:\mathbb{R} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\:\mathrm{2}{x}\:\rfloor\:\:+\:\lfloor\:\:\mathrm{3}{x}\:\rfloor\:=\:\mathrm{1} \\ $$$$\: \\ $$$$\:\:\:\:\lfloor\:{x}\:\rfloor\::=\:{greatest}\:{integer}\:{number} \\ $$$$\:\:\:\:{more}\:{than}\:\:{or}\:{equal}\:\:{to}\:\:''\:{x}\:'' \\ $$ Answered…

Question-185982

Question Number 185982 by Shrinava last updated on 30/Jan/23 Answered by Mathspace last updated on 30/Jan/23 $${we}\:{developp}\:{first}\:\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}} \\ $$$$=\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} {C}_{\mathrm{2}{n}} ^{{k}} {x}^{{k}} \:\:{but} \\…

Question-185972

Question Number 185972 by Michaelfaraday last updated on 30/Jan/23 Answered by Rasheed.Sindhi last updated on 30/Jan/23 $${x}=\sqrt[{\mathrm{3}}]{{p}}\:+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{p}}\:}\:,\:{y}=\sqrt{{p}}\:+\frac{\mathrm{1}}{\:\sqrt{{p}}\:} \\ $$$${Show}\:{that}\:\:\:{y}^{\mathrm{2}} −\mathrm{2}={x}\left({x}^{\mathrm{2}} −\mathrm{3}\right) \\ $$$${x}^{\mathrm{3}} =\left(\sqrt[{\mathrm{3}}]{{p}}\:+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{p}}\:}\right)^{\mathrm{3}} ={p}+\frac{\mathrm{1}}{{p}}+\mathrm{3}\left(\sqrt[{\mathrm{3}}]{{p}}\:+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{p}}\:}\right)…