U POJILIVOJUI 15. Find the number o...
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U POJILIVOJUI 15. Find the number of real values of x satisfying the equation 2 sin X = X+.

JEE/Engineering Exams
Maths
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( 2 sin x=x+frac{1}{x} ) ( 2 sin x=frac{x^{2}+1}{x} Rightarrow x^{2}-2 x sin x+1=0 ) ( Rightarrow frac{-b^{2} pm sqrt{b^{2}-4 a c}}{2 a} Rightarrow frac{2 sin x pm sqrt{(2 sin x)^{2}-400 a}}{2 c 1} ) ( Rightarrow quad frac{2 sin x pm sqrt{4 sin ^{2} x-4}}{2}=frac{2 sin x pm 2 sqrt{sin ^{2} x-1}}{2} ) ( therefore x=sin x+i cos x cos 3 sin x-operatorname{icos} x )
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