Category: Algebra

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 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}}…

Question Number 78040 by Pratah last updated on 13/Jan/20 Commented by mr W last updated on 13/Jan/20 $${the}\:{same}\:{path}\:{as}\:{for} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}−\mathrm{1}=\mathrm{0} \\ $$ Commented by…

Question Number 77990 by peter frank last updated on 12/Jan/20 $${Find}\:{the}\:{equation}\:{to}\:{the} \\ $$$${two}\:{circles}\:{each}\:{of} \\ $$$${which}\:{touch}\:{the}\:{three}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}{a}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{ax}=\mathrm{0} \\ $$$${x}^{\mathrm{2}}…

Question Number 12446 by tawa last updated on 22/Apr/17 $$\mathrm{find}\:\mathrm{x} \\ $$$$\sqrt{\mathrm{x}}\:\:=\:\:\mathrm{8}^{\mathrm{x}} \\ $$ Commented by mrW1 last updated on 23/Apr/17 $${For}\:{equation}\:\sqrt{{x}}={a}^{{x}} \:{the}\:{solution}\:{is} \\ $$$${x}=−\frac{{W}\left(−\mathrm{2ln}\:{a}\right)}{\mathrm{2ln}\:{a}}…