Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
2871 Upvotes
Verified Answer
The correct answer is:
$x+y=3, x-y=-3$
$\begin{gathered}\text { Given, } x^2-3|x|+2=0 \\ \qquad \begin{array}{c}(|x|-2)(|x|-1)=0 \\ |x|=2 \text { or }|x|=1 \\ x= \pm 2 \text { or } x= \pm 1\end{array}\end{gathered}$
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, $\quad x+y=0, x-y=0$
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, $\quad x+y=0, x-y=0$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.