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Question-62176

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Question Number 62176 by Tawa1 last updated on 16/Jun/19 Answered by MJS last updated on 17/Jun/19 $$\mathrm{to}\:\mathrm{make}\:\mathrm{it}\:\mathrm{clear}\:\mathrm{let}:\:{a},\:{b},\:{c},\:{d}\:\in\mathbb{R} \\ $$$${a}+{b}+{c}+{d}=\mathrm{1} \\ $$$${F}={ab}+{bc}+{cd} \\ $$$$ \\ $$$${d}=\mathrm{1}−{a}−{b}−{c}…

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dx-ydy-x-2-ydy-

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Question Number 127706 by arash sharifi last updated on 01/Jan/21 $${dx}+{ydy}={x}^{\mathrm{2}} {ydy} \\ $$ Answered by liberty last updated on 01/Jan/21 $$\:\mathrm{dx}\:=\:\mathrm{y}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{dy} \\ $$$$\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}}…

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Prove-without-induction-that-1-2-2n-1-2-2n-is-even-for-every-natural-number-n-

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Question Number 62169 by Tawa1 last updated on 16/Jun/19 $$\mathrm{Prove}\:\mathrm{without}\:\mathrm{induction}\:\mathrm{that}:\:\:\left(\mathrm{1}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:+\:\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:\:\mathrm{is}\:\mathrm{even}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\mathrm{n}.\:\:\: \\ $$ Answered by ajfour last updated on 16/Jun/19 $$\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}} +\left(\mathrm{1}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}}…

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2-1-3-

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Question Number 62140 by hhghg last updated on 15/Jun/19 $$\mathrm{2}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by Rio Michael last updated on 16/Jun/19 $$\mathrm{2}×\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{6} \\ $$ Terms of…

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