3. Решить уравнение arcsin(x)+arcsin(x/2)=pi/4 

[latex]arcsin(x)+arcsin( \frac{x}{2})= \frac{ \pi}{4} [/latex] [latex]x=sin(a); x/2=sin(b);[/latex] [latex] \left \{ {{a+b= \frac{ \pi}{4} } \atop {sin(a)=2*sin(b)}} \right. [/latex] [latex]sin(a)=2sin(\frac{ \pi }{4}-a)[/latex] [latex]sin(a)= \sqrt{2}(cos(a)-sin(a)[/latex]) [latex] \frac{1}{ \sqrt{2} } =ctg(x)-1[/latex] [latex]ctg(a)= \frac{\sqrt{2}-2 }{2} [/latex] [latex] \frac{ +-\sqrt{1- x^{2}} }{x} = \frac{\sqrt{2}-2 }{2} [/latex] [latex]4-4 x^{2} =6 x^{2} -4 \sqrt{2} x^{2} [/latex] [latex] x^{2} = \frac{4}{10-4 \sqrt{2} } [/latex] [latex] x = +- \sqrt{\frac{4}{10-4 \sqrt{2} } }[/latex]