Category: Algebra

Question Number 126165 by TheMexicanTacosG last updated on 17/Dec/20 $${if}:\:\:\:{b}^{\mathrm{2}} \:=\:−\mathrm{3}\:−{c}^{\mathrm{2}} \:+\mathrm{2}\left({a}−{b}−{c}\right)\:−{a}^{\mathrm{2}} \\ $$$$ \\ $$$${calculate}:\:{a}\:+\:{b}\:+\:{c}\:=\:? \\ $$ Commented by PRITHWISH SEN 2 last updated…

Question Number 191675 by MATHEMATICSAM last updated on 28/Apr/23 $$\mathrm{Solve}\:\mathrm{for}\:{x}\:: \\ $$$$\left({x}\:−\:\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:{x} \\ $$ Commented by mehdee42 last updated on 29/Apr/23 $${the}\:{graph}\:{of}\:{the}\:{function}\:{is}\:{as}\:{follows}.{therefore}\:.{the}\:{given}\:\: \\…

Question Number 126109 by mnjuly1970 last updated on 17/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:{calculus}… \\ $$$$\:\:{verify}\:\:{that}\:::\:\:\mathrm{A}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:{is} \\ $$$$\:\:\:\:\:\:{a}\:\:{rational}\:\:{number}\:… \\ $$ Answered by som(math1967) last updated on 17/Dec/20 $$\frac{\sqrt[{\mathrm{3}}]{\mathrm{8}\left(\mathrm{2}+\sqrt{\left.\mathrm{5}\right)}\right.}}{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)×\mathrm{2}} \\…

Question Number 126105 by Mathgreat last updated on 17/Dec/20 $$\mathrm{1}\leqslant{a};{b};{c};{d}\leqslant\mathrm{2} \\ $$$$\mid\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)\left(\mathrm{1}−{d}\right)\mid\leqslant\frac{{abcd}}{\mathrm{4}} \\ $$ Commented by Mathgreat last updated on 17/Dec/20 $$\boldsymbol{{prove}} \\ $$ Answered…

Question Number 191631 by Spillover last updated on 27/Apr/23 $$\int_{\mathrm{0}} ^{\infty} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {e}^{−{x}^{\mathrm{2}} } {dx} \\ $$ Answered by malwan last updated on 28/Apr/23 $${put}\:{x}^{\mathrm{2}}…