Modulue equation.

\hspace{-16}(1)::\;$Solve for $\mathbf{x\in\mathbb{R}$ in $\mathbf{\mid x^3-1\mid +\mid 2-x^3\mid = 1}}

2 Answers

Replace x³ by t.

Therefore,

\left|t-1 \right|+\left|2-t \right|=1

For t\leq1 ,

t=1

For 1<t<2 , the equation is satisfied \forall \: t \in \left(1,2 \right).

For t\geq2 ,

t=2

Then, solution set is given by \left\{f(x):f(x)=x^{\frac{1}{3}}, f:\left[1,2 \right]\rightarrow \mathbb{R} \right\}

@ashish: a better solution

|a|+|b|=|a+b|

this is true only if a and b are of the same sign.

Rest ur solution will follow.

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