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Category: Arithmetic

solve-to-z-2-x-2-y-2-24-

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Question Number 64153 by meme last updated on 14/Jul/19 $${solve}\:{to}\:{z}^{\mathrm{2}} \:\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{24} \\ $$ Answered by mr W last updated on 15/Jul/19 $$\left({x}−{y}\right)\left({x}+{y}\right)=\mathrm{24}={a}×{b}=\mathrm{1}×\mathrm{24}=\mathrm{2}×\mathrm{12}=\mathrm{3}×\mathrm{8}=\mathrm{4}×\mathrm{6} \\…

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Question-63561

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Question Number 63561 by aliesam last updated on 05/Jul/19 Answered by MJS last updated on 05/Jul/19 $$=\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)×\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\mathrm{2}{k}= \\ $$$$=\left[\mathrm{1}×\mathrm{3}×\mathrm{5}×…×\left(\mathrm{2}{n}−\mathrm{1}\right)\right]×\left[\mathrm{2}×\mathrm{4}×\mathrm{6}×…×\mathrm{2}{n}\right]= \\ $$$$=\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}×…×\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}\right)=…

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Given-U-n-2n-1-n-even-3n-3-n-odd-The-value-of-U-3-U-6-U-7-U-10-U-11-U-14-U-27-U-28-

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Question Number 128907 by bramlexs22 last updated on 11/Jan/21 $$\:\mathrm{Given}\:\mathrm{U}_{\mathrm{n}} \:=\:\begin{cases}{\mathrm{2n}+\mathrm{1}\:;\:\mathrm{n}\:\mathrm{even}}\\{\mathrm{3n}+\mathrm{3}\:;\:\mathrm{n}\:\mathrm{odd}}\end{cases} \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{U}_{\mathrm{3}} +\mathrm{U}_{\mathrm{6}} +\mathrm{U}_{\mathrm{7}} +\mathrm{U}_{\mathrm{10}} +\mathrm{U}_{\mathrm{11}} + \\ $$$$\:\mathrm{U}_{\mathrm{14}} +…+\mathrm{U}_{\mathrm{27}} +\mathrm{U}_{\mathrm{28}} =? \\ $$…

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