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sin-9x-sin-5x-sin-3x-find-x-

Question Number 211657 by hardmath last updated on 15/Sep/24 $$\mathrm{sin}\left(\mathrm{9x}\right)\:=\:\mathrm{sin}\left(\mathrm{5x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right) \\ $$$$\mathrm{find}:\:\:\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 15/Sep/24 $$\mathrm{sin}\:\left(\left(\mathrm{2}{n}+\mathrm{1}\right){x}\right)\:=\mathrm{sin}\:{x}\:\left(\mathrm{1}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{cos}\:\left(\mathrm{2}{kx}\right)\right) \\…

Question-211658

Question Number 211658 by efronzo1 last updated on 15/Sep/24 $$\:\:\:\underbrace{\:} \\ $$ Answered by mehdee1342 last updated on 15/Sep/24 $${y}=\sqrt{\mathrm{19}−\mathrm{8}\sqrt{\mathrm{3}}}\Rightarrow{y}^{\mathrm{2}} =\mathrm{19}−\mathrm{8}\sqrt{\mathrm{3}} \\ $$$${y}^{\mathrm{4}} −\mathrm{18}{y}^{\mathrm{2}} +\mathrm{361}=\mathrm{192}…

certificate-h-L-p-p-0-h-x-p-dx-

Question Number 211627 by MrGaster last updated on 15/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mid\mid\boldsymbol{{h}}\mid\mid_{\:^{\boldsymbol{{L}}^{\boldsymbol{{p}}} } } ^{\boldsymbol{{p}}} =\int_{\mathrm{0}} ^{\infty} \mid\boldsymbol{{h}}\left(\boldsymbol{{x}}\right)\mid^{\boldsymbol{{p}}} \boldsymbol{{dx}}. \\ $$…

In-triangle-ABC-C-60-If-the-length-of-opposite-sides-of-A-B-and-C-are-a-b-and-c-respectively-then-prove-that-1-a-c-1-b-c-3-a-b-c-

Question Number 211651 by MATHEMATICSAM last updated on 15/Sep/24 $$\mathrm{In}\:\mathrm{triangle}\:\mathrm{ABC},\:\angle\mathrm{C}\:=\:\mathrm{60}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{opposite}\:\mathrm{sides}\:\mathrm{of}\:\angle\mathrm{A},\:\angle\mathrm{B}\:\mathrm{and}\:\angle\mathrm{C}\:\mathrm{are} \\ $$$${a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{respectively}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}\:+\:{c}}\:+\:\frac{\mathrm{1}}{{b}\:+\:{c}}\:=\:\frac{\mathrm{3}}{{a}\:+\:{b}\:+\:{c}}\:. \\ $$ Answered by som(math1967) last updated on 15/Sep/24…

2x-4-4x-3-22x-2-24x-36-0-

Question Number 211597 by MrGaster last updated on 14/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}^{\mathrm{4}} −\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{22}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{x}}+\mathrm{36}=\mathrm{0} \\ $$$$ \\ $$ Answered by Ghisom last updated on…

x-2-4x-3-lt-0-2x-1-x-2-1-

Question Number 211598 by MrGaster last updated on 14/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{3}<\mathrm{0}}\\{\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{1}}{\boldsymbol{{x}}+\mathrm{2}}\geq\mathrm{1}}\end{cases} \\ $$$$ \\ $$ Answered by A5T last updated on 14/Sep/24 $${x}^{\mathrm{2}}…