Menu Close

Question-197310




Question Number 197310 by sonukgindia last updated on 13/Sep/23
Answered by Frix last updated on 13/Sep/23
(1) z^2 −7z+11=1  ⇒ z=2∨z=5  (2) ln (z^2 −3z+e^2 ) =0  ⇒ z=(3/2)∓((√(4e^2 −13))/2)i  (3) z^2 −7z+11=−1∧ln (z^2 −3z+e^2 ) =2n  ⇒ z=3
$$\left(\mathrm{1}\right)\:{z}^{\mathrm{2}} −\mathrm{7}{z}+\mathrm{11}=\mathrm{1} \\ $$$$\Rightarrow\:{z}=\mathrm{2}\vee{z}=\mathrm{5} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{ln}\:\left({z}^{\mathrm{2}} −\mathrm{3}{z}+\mathrm{e}^{\mathrm{2}} \right)\:=\mathrm{0} \\ $$$$\Rightarrow\:{z}=\frac{\mathrm{3}}{\mathrm{2}}\mp\frac{\sqrt{\mathrm{4e}^{\mathrm{2}} −\mathrm{13}}}{\mathrm{2}}\mathrm{i} \\ $$$$\left(\mathrm{3}\right)\:{z}^{\mathrm{2}} −\mathrm{7}{z}+\mathrm{11}=−\mathrm{1}\wedge\mathrm{ln}\:\left({z}^{\mathrm{2}} −\mathrm{3}{z}+\mathrm{e}^{\mathrm{2}} \right)\:=\mathrm{2}{n} \\ $$$$\Rightarrow\:{z}=\mathrm{3} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *