д) у² = 52у – 576; e) 15y² – 30 = 22y + 7; ж) 25р² = 10p – 1; з) 299x² + 100x = 500 – 101x².

д) $$y^2 = 52y - 576$$

$$y^2-52y+576=0$$

$$D=(-52)^2-4*1*576=2704-2304=400$$

$$y_1=\frac{52+\sqrt{400}}{2*1}=\frac{52+20}{2}=36$$

$$y_2=\frac{52-\sqrt{400}}{2*1}=\frac{52-20}{2}=16$$

Ответ: $$y_1=36; y_2=16$$

e) $$15y^2 - 30 = 22y + 7$$

$$15y^2-22y-37=0$$

$$D=(-22)^2-4*15*(-37)=484+2220=2704$$

$$y_1=\frac{22+\sqrt{2704}}{2*15}=\frac{22+52}{30}=2.46$$

$$y_2=\frac{22-\sqrt{2704}}{2*15}=\frac{22-52}{30}=-1$$

Ответ: $$y_1=2.46; y_2=-1$$

ж) $$25p^2 = 10p - 1$$

$$25p^2-10p+1=0$$

$$D=(-10)^2-4*25*1=100-100=0$$

$$p=\frac{10+\sqrt{0}}{2*25}=\frac{10}{50}=0.2$$

Ответ: $$p=0.2$$

з) $$299x^2 + 100x = 500 - 101x^2$$

$$400x^2+100x-500=0$$

$$4x^2+x-5=0$$

$$D=1^2-4*4*(-5)=1+80=81$$

$$x_1=\frac{-1+\sqrt{81}}{2*4}=\frac{-1+9}{8}=1$$

$$x_2=\frac{-1-\sqrt{81}}{2*4}=\frac{-1-9}{8}=-1.25$$

Ответ: $$x_1=1; x_2=-1.25$$