The product of integral solution of the equation is then find the value of .

JEE MainMathematicsToughInequalities and absolute value

The product of integral solution of the equation
$|||x - 1| - 2| - 1| = 2$ is $- \lambda$ then find the value of
$\lambda$ .

Show answer and solution

|||x - 1| - 2| - 1| = 2

\Rightarrow ||x - 1| - 2| - 1 = 2

||x - 1| - 2| - 1 = - 2

||x - 1| - 2| = 3

........(1) or

||x - 1| - 2| = - 1

Not possible
Case: 1

\mid (x - 1| - 2| = 3

\Rightarrow |x - 1| - 2 = 3

|x - 1| - 2 = - 3

\Rightarrow |x - 1| = 5

|x - 1| = - 1

\Rightarrow x - 1 = \pm 5

\Rightarrow x = 5 + 1, - 5 + 1

Not possible
= 6, - 4
Product of integral solutions

= 6 \times ( - 4)

= - 24

\Rightarrow \lambda = 24

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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