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Category: Algebra

2x-3-x-3-3-3-x-2-

Question Number 224770 by Abdulazim last updated on 03/Oct/25 $$\:\:\:\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−\mathrm{3}\right)^{\mathrm{3}} =\mathrm{3}−{x}^{\mathrm{2}} \\ $$ Commented by Ghisom_ last updated on 04/Oct/25 $$\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$ Terms…

Question-224763

Question Number 224763 by behi834171 last updated on 02/Oct/25 Commented by Ghisom_ last updated on 03/Oct/25 $$\mathrm{min}\:{f}\left({x},\:{y}\right)\:\mathrm{is}\:\approx\mathrm{3}.\mathrm{67113410}\:\mathrm{at} \\ $$$$\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\begin{pmatrix}{\frac{\mathrm{5}\sqrt{\mathrm{6}}−\mathrm{3}\sqrt{\mathrm{5}}}{\mathrm{7}}}\\{\mathrm{3}\sqrt{\mathrm{10}}−\mathrm{5}\sqrt{\mathrm{3}}}\end{pmatrix} \\ $$ Commented by behi834171 last…

Prove-that-sin-54-5-1-4-

Question Number 224635 by hardmath last updated on 23/Sep/25 $$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{sin}\left(\mathrm{54}°\right)\:=\:\:\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\mathrm{4}} \\ $$ Answered by som(math1967) last updated on 23/Sep/25 $$\:{let}\:\mathrm{54}=\alpha \\ $$$$\therefore\mathrm{5}\alpha=\mathrm{270} \\ $$$$\Rightarrow\mathrm{3}\alpha=\mathrm{270}−\mathrm{2}\alpha \\…

A-binary-operation-is-defined-on-a-set-real-numbers-R-by-x-y-2x-2y-xy-3-find-i-The-inverse-of-x-under-the-operation-ii-Truth-set-when-m-7-2-m-

Question Number 224614 by necx122 last updated on 21/Sep/25 $${A}\:{binary}\:{operation}\:\ast\:{is}\:{defined}\:{on}\:{a}\:{set} \\ $$$${real}\:{numbers},\:{R}\:{by} \\ $$$${x}\ast{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:−\frac{{xy}}{\mathrm{3}}\:. \\ $$$${find}: \\ $$$$\left({i}\right)\:{The}\:{inverse}\:{of}\:{x}\:{under}\:{the}\:{operation}\:\ast \\ $$$$\left({ii}\right)\:{Truth}\:{set}\:{when}\:{m}\ast\mathrm{7}=−\mathrm{2}\ast{m} \\ $$ Answered by hfdghcdfj…

p-is-a-prime-number-prove-that-if-p-2-8-is-prime-p-3-4-is-also-prime-

Question Number 224591 by Jyrgen last updated on 22/Sep/25 $$\mathrm{p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${prove}\:{that}\:{if}\:\mathrm{p}^{\mathrm{2}} +\mathrm{8}\:{is}\:{prime}\:\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:{p}^{\mathrm{3}} +\mathrm{4}\:{is}\:{also}\:{prime} \\ $$ Answered by Ghisom_ last updated on 22/Sep/25…

Question-224570

Question Number 224570 by Abdulazim last updated on 19/Sep/25 Answered by fantastic last updated on 19/Sep/25 $$\mathrm{30}^{\mathrm{0}} \\ $$$${AB}=\mathrm{2}{R}\mathrm{sin}\:\alpha \\ $$$${CH}=\mathrm{2}{R}\mathrm{cos}\:\alpha\left[{R}={circumradius}\right] \\ $$$${CH}=\sqrt{\mathrm{3}}{AB} \\ $$$$\mathrm{2}{R}\mathrm{cos}\:\alpha=\sqrt{\mathrm{3}}×\mathrm{2}{R}\mathrm{sin}\:\alpha…