Question

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

Answer 1

$2arcsin^2x-arcsin x-6=0 \\t = arcsin x \\2t^2-t -6=0 \\D = 1+6cdot4cdot2 = 49=7^2 \\t_1 = frac{1-7}{4}=-1,5 \\t_2 = frac{1+7}{4}=2$

 
$arcsin x = -1,5 \\arcsin x = 2$

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


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

Answer 2