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Question Number 185126 by Shrinava last updated on 17/Jan/23

(∣y∣−∣x∣−2,8)(∣x∣−∣y∣−1,8) = 0  ∣y∣ = a ∣x∣ + a ∣∣x∣ − 1,1∣ + 5  At what value of  a  does the equation  have  4  roots?

$$\left(\mid\mathrm{y}\mid−\mid\mathrm{x}\mid−\mathrm{2},\mathrm{8}\right)\left(\mid\mathrm{x}\mid−\mid\mathrm{y}\mid−\mathrm{1},\mathrm{8}\right)\:=\:\mathrm{0} \\ $$$$\mid\mathrm{y}\mid\:=\:\mathrm{a}\:\mid\mathrm{x}\mid\:+\:\mathrm{a}\:\mid\mid\mathrm{x}\mid\:−\:\mathrm{1},\mathrm{1}\mid\:+\:\mathrm{5} \\ $$$$\mathrm{At}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{have}\:\:\mathrm{4}\:\:\mathrm{roots}? \\ $$

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