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Q-1-x-2-y-2-i-2x-y-2i-Q-2-2-3i-x-2-3-x-y-2x-3y-




Question Number 10721 by niraj last updated on 23/Feb/17
Q.1  x^2 −y^2 −i(2x+y)=2i  Q.2   (2+3i)x^2 −(3−x)y=2x−3y
$${Q}.\mathrm{1}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{i}\left(\mathrm{2}{x}+{y}\right)=\mathrm{2}{i} \\ $$$${Q}.\mathrm{2}\:\:\:\left(\mathrm{2}+\mathrm{3}{i}\right){x}^{\mathrm{2}} −\left(\mathrm{3}−{x}\right){y}=\mathrm{2}{x}−\mathrm{3}{y} \\ $$
Answered by sandy_suhendra last updated on 23/Feb/17
Q.1  x^2 −y^2 =0  (x+y)(x−y)=0   x+y=0          or    x−y=0   x=−y ...(1)         x=y ...(2)    2x+y=−2 ⇒ substitute (1)  −2y+y=−2  y=2 ⇒ x=−2    2x+y=−2 ⇒ substitute (2)  2y+y=−2  y=−(2/3) ⇒ x=−(2/3)
$$\mathrm{Q}.\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{0} \\ $$$$\:\mathrm{x}+\mathrm{y}=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{or}\:\:\:\:\mathrm{x}−\mathrm{y}=\mathrm{0} \\ $$$$\:\mathrm{x}=−\mathrm{y}\:…\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{y}\:…\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\mathrm{2x}+\mathrm{y}=−\mathrm{2}\:\Rightarrow\:\mathrm{substitute}\:\left(\mathrm{1}\right) \\ $$$$−\mathrm{2y}+\mathrm{y}=−\mathrm{2} \\ $$$$\mathrm{y}=\mathrm{2}\:\Rightarrow\:\mathrm{x}=−\mathrm{2} \\ $$$$ \\ $$$$\mathrm{2x}+\mathrm{y}=−\mathrm{2}\:\Rightarrow\:\mathrm{substitute}\:\left(\mathrm{2}\right) \\ $$$$\mathrm{2y}+\mathrm{y}=−\mathrm{2} \\ $$$$\mathrm{y}=−\frac{\mathrm{2}}{\mathrm{3}}\:\Rightarrow\:\mathrm{x}=−\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$

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