Question Number 62184 by aliesam last updated on 17/Jun/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{3}{x}+\mathrm{1}}\:=\:\mathrm{3}\sqrt[{\mathrm{4}}]{{x}} \\ $$ Commented by MJS last updated on 17/Jun/19 $${x}=\mathrm{0}\:\vee\:{x}=\mathrm{1} \\ $$$$\mathrm{trying}\:\mathrm{2}{x}−\mathrm{1}={n}^{\mathrm{3}} \:\Rightarrow\:{x}=\frac{{n}^{\mathrm{3}} +\mathrm{1}}{\mathrm{2}} \\…
Question Number 127716 by liberty last updated on 01/Jan/21 $$\:\mathrm{Let}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{be}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{such}\:\mathrm{that}\:\begin{cases}{\mathrm{p}\sqrt{\mathrm{p}}\:+\mathrm{q}\sqrt{\mathrm{q}}\:=\:\mathrm{32}}\\{\mathrm{p}\sqrt{\mathrm{q}}\:+\:\mathrm{q}\sqrt{\mathrm{p}}\:=\:\mathrm{31}}\end{cases} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{5}\left(\mathrm{p}+\mathrm{q}\right)?}{\mathrm{7}} \\ $$ Answered by mindispower last updated on 01/Jan/21 $$\left(\sqrt{{p}}+\sqrt{{q}}\right)^{\mathrm{3}} ={p}\sqrt{{p}}+{q}\sqrt{{q}}+\mathrm{3}\left({p}\sqrt{{q}}+{p}\sqrt{{q}}\right)=\mathrm{32}+\mathrm{3}.\mathrm{31}=\mathrm{125}…
Question Number 62176 by Tawa1 last updated on 16/Jun/19 Answered by MJS last updated on 17/Jun/19 $$\mathrm{to}\:\mathrm{make}\:\mathrm{it}\:\mathrm{clear}\:\mathrm{let}:\:{a},\:{b},\:{c},\:{d}\:\in\mathbb{R} \\ $$$${a}+{b}+{c}+{d}=\mathrm{1} \\ $$$${F}={ab}+{bc}+{cd} \\ $$$$ \\ $$$${d}=\mathrm{1}−{a}−{b}−{c}…
Question Number 127706 by arash sharifi last updated on 01/Jan/21 $${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} \\ $$$$\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}}…
Question Number 62169 by Tawa1 last updated on 16/Jun/19 $$\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 $$\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}} +\left(\mathrm{1}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}}…
Question Number 62142 by hhghg last updated on 15/Jun/19 $$\mathrm{6}.\mathrm{38}\boldsymbol{\div}\mathrm{0}.\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62140 by hhghg last updated on 15/Jun/19 $$\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} \\ $$ Terms of…
Question Number 62137 by hhghg last updated on 15/Jun/19 $$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62138 by hhghg last updated on 15/Jun/19 $$\mathrm{5}^{\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62136 by hhghg last updated on 15/Jun/19 $$\mathrm{3}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com