The number of real solutions of the equation x x+3 x-1 -2 is: [2026]

Question

The number of real solutions of the equation $x$ $| x + 3 |$ $+$ $| x - 1 |$ $- 2 = 0$ is: [2026]

Smart Achievers · Accepted Answer

(1)

$(I)$

$x^{2} + 3 x + x - 1 - 2 = 0$

$x^{2} + 4 x - 3 = 0$

$x = - 2 + \sqrt{7} (rejected), - 2 - \sqrt{7} (rejected)$

$(II)$

$x^{2} + 3 x + 1 - x - 2 = 0$

$x^{2} + 2 x - 1 = 0$

$x = - 1 + \sqrt{2}, - 1 - \sqrt{2}$

$(III)$

$- x^{2} - 3 x + 1 - x - 2 = 0$

$x^{2} + 4 x + 1 = 0$

$x = - 2 - \sqrt{3}, - 2 + \sqrt{3} (rejected)$

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