If the lines drawn along the diagonals of the two squares formed by two pairs of lines $x^2-3|x|+2=0$ and $y^2-3 y+2=0$ form a square $A B C D$, then the equations of two adjacent sides of the square $A B C D$ are

• A

  $x+y=-3, x-y=3$
• B

  $x+y=0, x-y=3$
• Correct answer
  C

  $x+y=3, x-y=-3$
• D

  $x-y=0, x+y=-3$

Solution

$\begin{gathered}\text { Given, } x^2-3|x|+2=0 \\ \qquad \begin{array}{c}(|x|-2)(|x|-1)=0 \\ |x|=2 \text { or }|x|=1 \\ x= \pm 2 \text { or } x= \pm 1\end{array}\end{gathered}$ and $\begin{aligned} y^2-3 y+2 & =0 \\ (y-2)(y-1) & =0 \\ y & =2,1 \end{aligned}$ $\Rightarrow$
Equation of diagonal are $B^{\prime} D^{\prime}=x-y=0$ Equation of diagonal $A^{\prime} C^{\prime}=x+y=3$ Equation of diagonal $A C=x+y=0$ Equation of diagonal $B D=x-y+3=0$ $\therefore$ Equation of adjacent sides of square is possible Ist square, $\quad x+y=3, x-y+3=0$ IInd square, $\quad x+y=0, x-y=0$

Hence, the correct answer is option: 'C'.