Question Number 110722 by ZiYangLee last updated on 30/Aug/20
Answered by ajfour last updated on 30/Aug/20
$$\left({a}−{b}\right){x}+\left({b}−{a}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:{x}=\mathrm{1} \\ $$$$\Rightarrow\:\:{a}+{b}=−\mathrm{1}\:. \\ $$
Answered by bobhans last updated on 30/Aug/20
$$\Leftrightarrow\:\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{x}^{\mathrm{2}} \\ $$$$\Leftrightarrow\:−\mathrm{b}−\mathrm{ax}\:=\:−\mathrm{bx}−\mathrm{a} \\ $$$$\Leftrightarrow\:\left(\mathrm{b}−\mathrm{a}\right)\mathrm{x}\:=\:\mathrm{b}−\mathrm{a}\:;\:\mathrm{b}\:\neq\:\mathrm{a}\: \\ $$$$\Leftrightarrow\:\mathrm{x}\:=\:\mathrm{1}\:\Rightarrow\mathrm{1}^{\mathrm{2}} +\mathrm{a}+\mathrm{b}\:=\:\mathrm{0};\:\mathrm{a}+\mathrm{b}\:=\:−\mathrm{1} \\ $$