Question Number 156400 by ajfour last updated on 10/Oct/21 Commented by ajfour last updated on 10/Oct/21 $$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:\:\:\mathrm{f}\left(\mathrm{z}\right)=\left(\mathrm{z}−\mathrm{a}\right)^{\mathrm{2}} +\mathrm{b} \\ $$$$\mathrm{is}\:\mathrm{obtainable}\:\mathrm{by}\:\mathrm{the}\:\mathrm{welded} \\ $$$$\mathrm{parabola}\:\mathrm{wires}\:\left(\mathrm{with}\:\mathrm{mutually}\right. \\ $$$$\mathrm{perpendicular}\:\mathrm{planes};\:\:\mathrm{upper} \\…
Question Number 25317 by ibraheem160 last updated on 08/Dec/17 $${solvd}\:{for}\:{x}:\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{4} \\ $$ Answered by ajfour last updated on 08/Dec/17 $${let}\:\:\:{u}=\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:\right)^{{x}} \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{ln}\:{u}={x}\mathrm{ln}\:\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}} \\…
Question Number 90842 by jagoll last updated on 26/Apr/20 $${x}^{\mathrm{2}} −\left({y}−{z}\right)^{\mathrm{2}} \:=\:\mathrm{3} \\ $$$${y}^{\mathrm{2}} \:−\:\left({z}−{x}\right)^{\mathrm{2}} \:=\:\mathrm{5} \\ $$$${z}^{\mathrm{2}} \:−\:\left({x}−{y}\right)^{\mathrm{2}} \:=\:\mathrm{12} \\ $$ Commented by john…
Question Number 156361 by mr W last updated on 10/Oct/21 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{1}}}\:=\mathrm{1}−\:\frac{\mathrm{2}}{\mathrm{x}} \\ $$ Commented by cortano last updated on 11/Oct/21 Commented by…
Question Number 156362 by MathSh last updated on 10/Oct/21 Answered by mindispower last updated on 10/Oct/21 $$\mid\Omega_{\mathrm{1}} +{i}\Omega_{\mathrm{2}} \mid^{\mathrm{2}} =\Omega_{\mathrm{1}} ^{\mathrm{2}} +\Omega_{\mathrm{2}} ^{\mathrm{2}} \\ $$$$\Omega_{\mathrm{1}}…
Question Number 25283 by Tinkutara last updated on 07/Dec/17 Commented by Tinkutara last updated on 07/Dec/17 $${Solve}\:{for}\:{x}. \\ $$ Answered by naka3546 last updated on…
Question Number 156359 by MathSh last updated on 10/Oct/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{3} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\left(\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{1}\right)\left(\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{1}\right)\left(\mathrm{c}^{\mathrm{3}} \:+\:\mathrm{1}\right)}\:\geqslant\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 25278 by Tinkutara last updated on 07/Dec/17 $${Find}\:{the}\:{number}\:{of}\:{solutions}\:{of} \\ $$$$\mathrm{log}\mid{x}\mid\:=\:{e}^{{x}} \\ $$ Commented by Tinkutara last updated on 08/Dec/17 $${Can}\:{it}\:{be}\:{solved}\:{using}\:{Lambert}'{s}\:{W} \\ $$$${function}? \\…
Question Number 156338 by MathSh last updated on 10/Oct/21 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{1}}}\:=\:\frac{\mathrm{2}}{\mathrm{x}}\:-\:\mathrm{1} \\ $$$$ \\ $$ Commented by mr W last updated on 10/Oct/21…
Question Number 156333 by MathSh last updated on 10/Oct/21 Answered by Rasheed.Sindhi last updated on 10/Oct/21 $$\underline{\mathrm{NOT}\:\mathrm{General}\:\mathrm{Solution}} \\ $$$$\mathrm{Simple}\:\mathrm{special}\:\mathrm{case}:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{x}_{\mathrm{1}} =\sqrt{\mathrm{x}_{\mathrm{1}} +\mathrm{22}}\:−\sqrt{\mathrm{x}_{\mathrm{1}} +\mathrm{1}}\: \\…