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no of sol. of Ix+2I+IxI+Ix-2I=p ,p belongs to Real no. are?

no of sol. of Ix+2I+IxI+Ix-2I=p ,p belongs to Real no. are?

Grade:12th pass

2 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-0.7 cm}$ We can write $|x-2| = |2-x|$\\\\ So $|x+2|+|2-x|\geq |x+2+2-x| = 4\;\forall x\in \left[-2,2\right]$\\\\ So $|x+2|+|x|+|x-2|\geq 4+|x|\geq 4$ and equality hold when $x=0$\\\\ So we get $|x+2|+|x|+|x-2|= p\geq 4$\\\\ So we get $p\in \left[ 4,\infty\right)$
Pranav Dabhade
34 Points
7 years ago
draw the graph of given eq. hence getting if p=4 we getone sol.i.e x=0 while for all p>4 two solutions.

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