Question Number 12621 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 $${one}\:{or}\:{more}\:{is}\:{true}.{find}\:{it}\:{or}\:{them}! \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 12623 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 $${one}\:{or}\:{more}\:{is}\:{true}.{find}\:{it}\:{or}\:{them}! \\ $$ Answered by prakash jain last updated…
Question Number 143684 by Huy last updated on 17/Jun/21 $$\mathrm{x}^{\mathrm{3}} +\mathrm{x}−\mathrm{1}=^{\mathrm{3}} \sqrt{\mathrm{2x}^{\mathrm{3}} +\mathrm{11}}+\sqrt{\mathrm{5x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$\mathrm{Find}\:\mathrm{x}\in\mathbb{R} \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21…
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Question Number 78108 by mr W last updated on 14/Jan/20 Commented by mr W last updated on 14/Jan/20 $${find}\:{the}\:{relation}\:{between}\:{a}\:{and}\:{c}. \\ $$$$ \\ $$$$\left({i}\:{reposted}\:{the}\:{question}\:{here}\:{to}\:{avoid}\right. \\ $$$${that}\:{the}\:{solution}\:{will}\:{be}\:{deleted}\:{by}…
Question Number 78102 by Pratah last updated on 14/Jan/20 Commented by MJS last updated on 14/Jan/20 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{for}\:{a},\:{b},\:{c},\:{d}\:\mathrm{with}\:\mathrm{any}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{as}\:\mathrm{parameter},\:\mathrm{then}\:\mathrm{calculate}\:\mathrm{the} \\ $$$$\mathrm{needed}\:\mathrm{values}\:\Rightarrow\:\mathrm{done}! \\ $$ Answered by…
Question Number 143597 by Videz last updated on 16/Jun/21 $${s}\:=\:{ut}\:+\:\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \:\:\Rightarrow\:\:{t}^{\mathrm{2}} \:+\:\mathrm{2}\frac{{u}}{{a}}{t}\:−\:\mathrm{2}\frac{{s}}{{a}}\:=\:\mathrm{0} \\ $$$${by}\:{the}\:{use}\:{of}\:{quadratic}\:{formula} \\ $$$${t}\:=\:\frac{−\frac{\mathrm{2}{u}}{{a}}\:\pm\:\sqrt{\frac{\mathrm{4}{u}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\mathrm{4}{s}}}{\mathrm{2}} \\ $$$${t}\:=\:−\frac{{u}}{{a}}\:\:\pm\:\:\sqrt{\frac{{u}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:{s}} \\ $$$${Victor}\:\:{Francis} \\…
Question Number 143591 by mathdanisur last updated on 16/Jun/21 $${a};{b};{c}>\mathrm{0}\:\:{and}\:\:{a}+{b}+{c}={k} \\ $$$$\boldsymbol{{min}}\left(\frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+{b}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+{c}^{\mathrm{2}} }\right)=? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jun/21 $$\mathrm{Let}\:{f}\left({a},{b},{c}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}}…
Question Number 143584 by Huy last updated on 16/Jun/21 $$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{7}}\\{\left({x}+\mathrm{3}\right)\left({y}−\mathrm{2}\right)=\sqrt{{xy}+\mathrm{3}}+\sqrt{{xy}−\mathrm{2}}}\end{cases} \\ $$$${Find}\:{x},{y} \\ $$ Answered by MJS_new last updated on 16/Jun/21 $$\mathrm{assuming}\:\mathrm{both}\:\sqrt{{xy}+\mathrm{3}}\:\mathrm{and}\:\sqrt{{xy}−\mathrm{2}}\:\mathrm{are}\:\in\mathbb{N} \\…
Question Number 143582 by ajfour last updated on 16/Jun/21 $${x}^{\mathrm{3}} −{x}−{c}=\mathrm{0} \\ $$$${let}\:\:{x}={t}+{h} \\ $$$$\left({t}−{s}\right)\left\{{t}^{\mathrm{3}} +\mathrm{3}{ht}^{\mathrm{2}} +\left(\mathrm{3}{h}^{\mathrm{2}} −\mathrm{1}\right){t}\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\left({h}^{\mathrm{3}} −{h}−{c}\right)\right\}=\mathrm{0} \\ $$$${let}\:{t}={p}+{q} \\ $$$$\left({p}+{q}−{s}\right)\left\{{p}^{\mathrm{3}}…