Question

arctg(2x)+arctg(3x)=3π/4. Determinati x.

Answer 1

Se cunoasc formulele: $tg(a+b)= \frac{tga+tgb}{1-tga*tgb}$; 
$tg(Arctgx)=tg(arctgx)=x$. Aplicam tangeta asupra egalitatii si ne rezulta ecuatia: $\frac{2x+3x}{1-2x*3x}=-1$. deci⇒$6 x^{2} -5x-1=0,$ care are radacinile $x_{1}=1, si. x_{2}=- \frac{1}{6}$.