Question

Решите уравнение 2arcsin^2-arcsinx-6=0

Answer 1

$2\arcsin^2x-\arcsin x-6=0 \\\\t = \arcsin x \\\\2t^2-t -6=0 \\\\D = 1+6\cdot4\cdot2 = 49=7^2 \\\\t_1 = \frac{1-7}{4}=-1,5 \\\\t_2 = \frac{1+7}{4}=2$

 
$\arcsin x = -1,5 \\\\\arcsin x = 2$

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$\arcsin x = -1,5 \\\\\sin(\arcsin x )=\sin(-1,5) \\\\x = \sin(-1,5)$

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$\arcsin x = 2 \\\\\sin(\arcsin x) = \sin2 \\\\x = \sin2$