88y = 77 - 99 [Отняли 99]
88y= -22
y = -22 / 88 [разделили на 88]
y = -1 / 4
y = -0.25
Найдем дискриминант квадратного уравнения
![D=(2a-4)^2-4a^2=(2a-4-2a)(2a-4+2a)=16(1-a)\\ \sqrt{D} =4 \sqrt{1-a}](https://tex.z-dn.net/?f=D%3D%282a-4%29%5E2-4a%5E2%3D%282a-4-2a%29%282a-4%2B2a%29%3D16%281-a%29%5C%5C+%5Csqrt%7BD%7D+%3D4+%5Csqrt%7B1-a%7D+)
![x=\dfrac{4-2a\pm4\sqrt{1-a} }{2a} = \dfrac{2-a\pm2\sqrt{1-a} }{a}= \\ \\ \\ = \dfrac{(\sqrt{1-a} )^2\pm2\sqrt{1-a} +1}{a}= \dfrac{(\sqrt{1-a} \pm 1)^2}{a}](https://tex.z-dn.net/?f=+x%3D%5Cdfrac%7B4-2a%5Cpm4%5Csqrt%7B1-a%7D+%7D%7B2a%7D+%3D+%5Cdfrac%7B2-a%5Cpm2%5Csqrt%7B1-a%7D+%7D%7Ba%7D%3D+%5C%5C+%5C%5C+%5C%5C+%3D+%5Cdfrac%7B%28%5Csqrt%7B1-a%7D+%29%5E2%5Cpm2%5Csqrt%7B1-a%7D+%2B1%7D%7Ba%7D%3D+%5Cdfrac%7B%28%5Csqrt%7B1-a%7D+%5Cpm+1%29%5E2%7D%7Ba%7D++)
По условию, нужно найти два различных решений больших или равных а.
![x \geq a\\ \\ \dfrac{(\sqrt{1-a} \pm1)^2}{a} \geq a](https://tex.z-dn.net/?f=x+%5Cgeq+a%5C%5C+%5C%5C++%5Cdfrac%7B%28%5Csqrt%7B1-a%7D+%5Cpm1%29%5E2%7D%7Ba%7D++%5Cgeq+a)
ОДЗ:
![(\sqrt{1-a} \pm 1)^2 \geq a^2\\ \\ (\sqrt{1-a} \pm 1)^2-a^2 \geq 0\\ \\ (\sqrt{1-a} \pm1-a)(\sqrt{1-a} \pm 1+a) \geq 0](https://tex.z-dn.net/?f=%28%5Csqrt%7B1-a%7D+%5Cpm+1%29%5E2+%5Cgeq+a%5E2%5C%5C+%5C%5C+%28%5Csqrt%7B1-a%7D+%5Cpm+1%29%5E2-a%5E2+%5Cgeq+0%5C%5C+%5C%5C+%28%5Csqrt%7B1-a%7D+%5Cpm1-a%29%28%5Csqrt%7B1-a%7D+%5Cpm+1%2Ba%29+%5Cgeq+0)
![a \in (-\infty;-3]\cup(0;1]](https://tex.z-dn.net/?f=a+%5Cin+%28-%5Cinfty%3B-3%5D%5Ccup%280%3B1%5D)
- решение для неравенства
![(\sqrt{1-a} +1-a)(\sqrt{1-a} + 1+a) \geq 0](https://tex.z-dn.net/?f=%28%5Csqrt%7B1-a%7D+%2B1-a%29%28%5Csqrt%7B1-a%7D+%2B+1%2Ba%29+%5Cgeq+0)
с учетом ОДЗ
![a \in (-\infty;0)](https://tex.z-dn.net/?f=a+%5Cin+%28-%5Cinfty%3B0%29)
- решение неравенства
![(\sqrt{1-a} -1-a)(\sqrt{1-a} -1+a) \geq 0](https://tex.z-dn.net/?f=%28%5Csqrt%7B1-a%7D+-1-a%29%28%5Csqrt%7B1-a%7D+-1%2Ba%29+%5Cgeq+0)
с учетом ОДЗ
Общее:
![a \in (-\infty;-3]](https://tex.z-dn.net/?f=a+%5Cin+%28-%5Cinfty%3B-3%5D)
Ответ:
![a \in (-\infty;-3]](https://tex.z-dn.net/?f=a+%5Cin+%28-%5Cinfty%3B-3%5D)
пятый член прогрессии - 1/27...........
Сos 2x= cos² x - sin² x = 2cos² t - 1
Sin² x + cos² x =1
(cos 2t - cos² t)/(1 - cos² t)= (cos² t - sin² t - cos² t)/ sin² t = - sin² t /sin² t = -1