(y+5)/(y^2-5y) -(y-5)/(2y^2-10y)=y+25/2y^2-50 решить уравнения!потом sina=1/sqrt 5 :...

Добавлю первое:
$\dfrac{y+5}{y(y-5)}-\dfrac{y-5}{2y(y-5)}=\dfrac{y+25}{2(y-5)(y+5)}$
$2(y+5)^2-(y^2-25)=y^2+25y$
$2y^2+20y+50-y^2+25-y^2-25y=0$
-5y=-75
y=15
Ответ: 15.
Добавлю второе:
$sin\ a=\dfrac{1}{\sqrt5}$
$1-cos\ 2a=1-(1-2sin^2a)=2sin^2a=2*(\frac{1}{\sqrt5})^2=2*\frac{1}{5}=\frac{2}{5}.$
На десерт:
10\\ 3x>5\\ x>1\frac{2}{3}" alt="15x^2-(5x-2)(3x+1)<7x-8\\ 15x^2-(15x^2-x-2)<7x-8\\ x+2<7x-8\\ 6x>10\\ 3x>5\\ x>1\frac{2}{3}" align="absmiddle" class="latex-formula">
Ответ: $(1\frac{2}{3};\ +\infty)$