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Category: Algebra

Question-199837

Question Number 199837 by Calculusboy last updated on 10/Nov/23 Answered by AST last updated on 10/Nov/23 $$\sqrt{{a}+\sqrt{{b}}}={p};\sqrt{{a}−\sqrt{{b}}}={q}\Rightarrow{p}^{\mathrm{2}} +{q}^{\mathrm{2}} =\mathrm{2}{a};{p}^{\mathrm{2}} {q}^{\mathrm{2}} ={a}^{\mathrm{2}} −{b} \\ $$$$\Rightarrow{pq}=\sqrt{{a}^{\mathrm{2}} −{b}}\Rightarrow\left({p}+{q}\right)^{\mathrm{2}}…

Question-199893

Question Number 199893 by hardmath last updated on 10/Nov/23 Commented by mr W last updated on 10/Nov/23 $${do}\:{you}\:{know}\:{what}\:{the}\:{question}\:{is}? \\ $$$${if}\:{you}\:{don}'{t}\:{know},\:{then}\:{other}\:{people} \\ $$$${don}'{t}\:{know}\:{either}. \\ $$$${badly}\:{prepared}\:{questions}\:{don}'{t} \\…

Question-199770

Question Number 199770 by Rupesh123 last updated on 09/Nov/23 Answered by aleks041103 last updated on 09/Nov/23 $${C}=\pi−\mathrm{3}\alpha \\ $$$$\Rightarrow\frac{\mathrm{5}}{{sin}\left(\mathrm{2}\alpha\right)}=\frac{\mathrm{6}}{{sin}\left(\pi−\mathrm{3}\alpha\right)}=\frac{\mathrm{6}}{{sin}\left(\mathrm{3}\alpha\right)} \\ $$$$\Rightarrow\mathrm{6}{sin}\left(\mathrm{2}\alpha\right)=\mathrm{5}{sin}\left(\mathrm{3}\alpha\right) \\ $$$${sin}\left(\mathrm{2}\alpha\right)=\mathrm{2}{sin}\left(\alpha\right){cos}\left(\alpha\right) \\ $$$${sin}\left(\mathrm{3}\alpha\right)={sin}\left(\mathrm{2}\alpha\right){cos}\left(\alpha\right)+{sin}\left(\alpha\right){cos}\left(\mathrm{2}\alpha\right)=…