Question Number 150313 by dany last updated on 11/Aug/21 Answered by ajfour last updated on 11/Aug/21 $${f}\left({x}−{y}\right)={f}\left({x}\right){f}\left({y}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−{f}\left({a}−{x}\right){f}\left({a}+{y}\right) \\ $$$${y}=\mathrm{0} \\ $$$$\cancel{{f}\left({x}\right)}=\cancel{{f}\left({x}\right)}−{f}\left({a}−{x}\right){f}\left({a}\right) \\ $$$$\Rightarrow\:\:{f}\left({a}−{x}\right)=\mathrm{0}\:\:{and}/{or}\:{f}\left({a}\right)=\mathrm{0}…
Question Number 150312 by naka3546 last updated on 11/Aug/21 $${Find}\:\:{n}\:\:{lowest}\:\:{integers}\:\:{that}\:\:{divide}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots+\:{n}^{\mathrm{2}} \right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150311 by naka3546 last updated on 11/Aug/21 $${x},{y}\:\in\:\mathbb{R} \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)\:\centerdot\:{f}\left({y}\right)\:−\:{f}\left({x}\:\centerdot\:{y}\right)\:+\:\mathrm{1} \\ $$$$ \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({f}\left({x}\right)\right)\:=\:{f}\left({x}\right)\:+\:{x} \\ $$ Answered by aleks041103…
Question Number 84767 by naka3546 last updated on 16/Mar/20 $${Find}\:\:{all}\:\:{solutions}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\mathrm{2020}{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\:=\:\:\mathrm{6059} \\ $$$${x},\:{y}\:<\:\:\mathrm{2020}\:\:,\:\:\:{x},\:{y}\:\:\in\:\:\mathbb{N} \\ $$ Answered by mr W last updated on…
Question Number 150299 by otchereabdullai@gmail.com last updated on 10/Aug/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{73}\:\mathrm{and}\:\mathrm{xy}=\mathrm{12}\:,\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \\ $$ Answered by cherokeesay last updated on 10/Aug/21 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 19194 by mondodotto@gmail.com last updated on 06/Aug/17 Answered by allizzwell23 last updated on 06/Aug/17 $$\:\:\:\:\:\left(\frac{\mathrm{25}}{\mathrm{4}}\:\right)^{\mathrm{3}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{4}}{\mathrm{10}}\right)^{\mathrm{3}\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{2}}{\mathrm{5}}\right)^{\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{−\left(\mathrm{5}−\mathrm{x}\right)} \\…
Question Number 19154 by khamizan833@yahoo.com last updated on 06/Aug/17 $$\mathrm{If}\:{f}\left({x}\right)\:=\:\frac{\mathrm{9}^{{x}} }{\mathrm{9}^{{x}} \:+\:\mathrm{3}},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2007}}\right)\:+\:{f}\left(\frac{\mathrm{2}}{\mathrm{2007}}\right)\:+\:{f}\left(\frac{\mathrm{3}}{\mathrm{2007}}\right)\:+\:…\:+\:{f}\left(\frac{\mathrm{2006}}{\mathrm{2006}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150222 by lapache last updated on 10/Aug/21 $${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =…..??\:\:\:\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =….??\:\:\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$$$ \\…
Question Number 84683 by M±th+et£s last updated on 15/Mar/20 $${x}\in{N}\:{and}\:{y}\in{N}:\left({x}<{y}\right) \\ $$$${slove}\:\left({E}\right): \\ $$$${xy}−\mathrm{4}{y}+\mathrm{3}{x}−\mathrm{2027}=\mathrm{0}…..\left({E}\right) \\ $$ Answered by mr W last updated on 15/Mar/20 $$\mathrm{4}<{x}<\mathrm{45}…
Question Number 150202 by tabata last updated on 10/Aug/21 $${lim}_{{x}\rightarrow\mathrm{2}} \left(\frac{\mathrm{16}−\mathrm{4}^{{x}} }{\mathrm{9}−\mathrm{3}^{{x}} }\right)\:{with}\:{out}\:{lophital} \\ $$ Commented by tabata last updated on 10/Aug/21 $$?????? \\ $$…