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Category: Algebra

Question-215052

Question Number 215052 by Abdullahrussell last updated on 27/Dec/24 Answered by mr W last updated on 27/Dec/24 f(1)=1f(x)=(x1)g(x)+1f(2)=(21)g(2)+1=4g(2)=3g(x)=(x2)h(x)+3f(x)=(x1)[(x2)h(x)+3]+1$${f}\left(\mathrm{3}\right)=\left(\mathrm{3}−\mathrm{1}\right)\left[\left(\mathrm{3}−\mathrm{2}\right){h}\left(\mathrm{3}\right)+\mathrm{3}\right]+\mathrm{1}=\mathrm{3}\:\Rightarrow{h}\left(\mathrm{3}\right)=−\mathrm{2}\:\Rightarrow{h}\left({x}\right)=\left({x}−\mathrm{3}\right){k}\left({x}\right)−\mathrm{2} \

Question-214888

Question Number 214888 by Emmanuel07 last updated on 22/Dec/24 Commented by mr W last updated on 23/Dec/24 igot$${a}_{{n}} =\mathrm{cot}\:\left\{\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}−\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+\frac{\pi}{\mathrm{8}}\right]\left(\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} −\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}−\frac{\mathrm{3}\pi}{\mathrm{8}}\right)−\frac{\pi}{\mathrm{8}}\right]\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} \right\}…