Question

The largest integral value of $k$ for which the equation $|x^2-4|x|+4|=k$ is satisfied by four distinct value of $x$.

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

Answer: (B)

$3$

$||x{|}^2-4|x|+4|=k$
$(|x|-2{)}^2=k$
From the above plot, for $x$ to have four distinct solutions, $k$ should satisfy the condition
$0<k<4$
Hence the largest integral value of $k$ satisfying the given constraints is $3$