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Category: Algebra

If-x-p-iq-h-ik-and-p-q-k-h-then-relate-p-q-h-k-R-such-that-x-R-

Question Number 199290 by ajfour last updated on 31/Oct/23 $${If}\:{x}=\sqrt{{p}+{iq}}+\sqrt{{h}+{ik}} \\ $$$${and}\:\:\frac{{p}}{{q}}\neq\frac{{k}}{{h}}\:\:{then}\:{relate}\:{p},{q},{h},{k}\:\in\mathbb{R} \\ $$$${such}\:{that}\:{x}\in\mathbb{R}. \\ $$ Commented by Frix last updated on 31/Oct/23 $$\sqrt{{x}+{y}\mathrm{i}}={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{with}\:{r}>\mathrm{0}\wedge−\frac{\pi}{\mathrm{2}}<\theta\leqslant\frac{\pi}{\mathrm{2}}…

Question-199259

Question Number 199259 by hardmath last updated on 30/Oct/23 Commented by Frix last updated on 30/Oct/23 $$\sqrt{\sqrt{\mathrm{12345689654321233}\pm\mathrm{5333334096}\sqrt{\mathrm{12345679}}}}= \\ $$$$=\sqrt{\mathrm{111111127}\pm\mathrm{24}\sqrt{\mathrm{12345679}}}= \\ $$$$=\pm\mathrm{4}+\mathrm{3}\sqrt{\mathrm{12345679}} \\ $$$$\sqrt[{\mathrm{3}}]{{x}−{y}}=\sqrt[{\mathrm{4}}]{\mathrm{8}}=\mathrm{2} \\ $$…

x-y-positive-real-numbers-If-15-x-9-y-Find-5-3x-2y-x-

Question Number 199230 by hardmath last updated on 29/Oct/23 $$\mathrm{x}\:,\:\mathrm{y}\::\:\:\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{If}\::\:\:\:\mathrm{15}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{9}^{\boldsymbol{\mathrm{y}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{5}^{\frac{\mathrm{3}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{y}}\:−\:\boldsymbol{\mathrm{x}}}} \:\:=\:\:? \\ $$ Answered by AST last updated on 29/Oct/23…

B-O-M-Each-is-a-distinct-positive-integer-If-B-O-M-223-Find-max-B-O-M-

Question Number 199183 by hardmath last updated on 29/Oct/23 $$\mathrm{B},\mathrm{O},\mathrm{M}\:-\:\mathrm{Each}\:\mathrm{is}\:\mathrm{a}\:\mathrm{distinct}\:\mathrm{positive} \\ $$$$\mathrm{integer} \\ $$$$\mathrm{If}\:\:\:\mathrm{B}\:\centerdot\:\mathrm{O}\:\centerdot\:\mathrm{M}\:=\:\mathrm{223} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{max}\left(\mathrm{B}\:+\:\mathrm{O}\:+\:\mathrm{M}\right)=? \\ $$ Answered by mr W last updated on…