Question Number 175871 by infinityaction last updated on 08/Sep/22 $$\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{13}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{14x}+\mathrm{130}} \\ $$$$\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:\mathrm{x}\:\in\:\mathbb{R}\: \\ $$ Answered by mr W last updated on 08/Sep/22 $${f}\left({x}\right)=\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{2}}…
Question Number 175860 by Shrinava last updated on 08/Sep/22 Answered by mr W last updated on 08/Sep/22 $${we}\:{know}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+…=\frac{\pi^{\mathrm{2}} }{\mathrm{6}}…
Question Number 44783 by Necxx last updated on 04/Oct/18 $$\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{97}…….\mathrm{1} \\ $$$$\left({x}^{\mathrm{2}} \right)^{\mathrm{3}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{3}} =\mathrm{793}…….\mathrm{2} \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$ Answered…
Question Number 110318 by Study last updated on 28/Aug/20 $$\left({a}+{b}−{c}\right)^{\mathrm{2}} =?? \\ $$ Answered by john santu last updated on 28/Aug/20 $$={a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}{ab}−\mathrm{2}{ac}−\mathrm{2}{bc}…
Question Number 175849 by Linton last updated on 08/Sep/22 $$\mathrm{2}^{\mathrm{2}{a}} +\mathrm{2}^{{a}} =\:\mathrm{10} \\ $$$${what}\:{is}\:{a}? \\ $$ Answered by MJS_new last updated on 08/Sep/22 $$\mathrm{2}^{\mathrm{2}{a}} +\mathrm{2}^{{a}}…
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Question Number 175839 by Rasheed.Sindhi last updated on 08/Sep/22 $${If}\:{w},\:{x},\:{y}\:{and}\:{z}\:{be}\:{four}\:{consecutive} \\ $$$${terms}\:{of}\:{any}\:{AP},\:{then}\:{show}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{w}^{\mathrm{2}} −{z}^{\mathrm{2}} =\mathrm{3}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right). \\ $$ Answered by mr W last…
Question Number 175838 by Rasheed.Sindhi last updated on 08/Sep/22 $${If}\:{x},{y}\:{and}\:{z}\:{be}\:{the}\:{pth},\:{qth}\:{and}\:{rth} \\ $$$${terms}\:{of}\:{an}\:{AP},\:{show}\:{that} \\ $$$$\begin{vmatrix}{{p}}&{{q}}&{{r}}\\{{x}}&{{y}}&{{z}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$ Answered by Rasheed.Sindhi last updated on 08/Sep/22 $$\begin{vmatrix}{{p}}&{{q}}&{{r}}\\{{x}}&{{y}}&{{z}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\end{vmatrix}=\mathrm{0} \\…
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Question Number 110299 by Lekhraj last updated on 28/Aug/20 Answered by Her_Majesty last updated on 28/Aug/20 $$\mathrm{5}{x}+\mathrm{5}{y}=\mathrm{2}{xy} \\ $$$$\Rightarrow\:\mathrm{5}\mid{xy}\:\Rightarrow\:\mathrm{5}\mid{x}\vee\mathrm{5}\mid{y} \\ $$$${let}\:{x}=\mathrm{5}{k} \\ $$$$\mathrm{25}{k}+\mathrm{5}{y}=\mathrm{10}{ky} \\ $$$${y}=\frac{\mathrm{5}{k}}{\mathrm{2}{k}−\mathrm{1}}…