Решение смотри на фотографии
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![\frac{x}{x + 5} + \frac{x + 5}{x - 5} = \frac{50}{ {x}^{2} - 25 }](https://tex.z-dn.net/?f=+%5Cfrac%7Bx%7D%7Bx+%2B+5%7D++%2B++%5Cfrac%7Bx+%2B+5%7D%7Bx+-+5%7D++%3D++%5Cfrac%7B50%7D%7B+%7Bx%7D%5E%7B2%7D+-+25+%7D+)
ОДЗ: х не равно +-5
Умножим в левой части первую дробь на х-5, а вторую - на х+5
![\frac{x(x - 5) + {(x + 5)}^{2} }{ {x}^{2} - 25 } = \frac{50}{ {x}^{2} - 25 } \: \: \: \: \: ( \times ({x}^{2} - 25)) \\ {x}^{2} - 5x + {x}^{2} + 10x + 25 = 50 \\ 2 {x}^{2} + 5x - 25 = 0 \\ D = 25 + 200 = 225 = 15 \\ x 1 = \frac{ - 5 + 15}{4} = \frac{10}{4} = 2.5 \\ x2 = \frac{ - 5 - 15}{4} = - 5](https://tex.z-dn.net/?f=+%5Cfrac%7Bx%28x++-+5%29+%2B++%7B%28x+%2B+5%29%7D%5E%7B2%7D+%7D%7B+%7Bx%7D%5E%7B2%7D+-+25+%7D++%3D++%5Cfrac%7B50%7D%7B+%7Bx%7D%5E%7B2%7D+-+25+%7D++%5C%3A++%5C%3A+++%5C%3A++%5C%3A++%5C%3A+%28+%5Ctimes++%28%7Bx%7D%5E%7B2%7D+-+25%29%29+%5C%5C++%7Bx%7D%5E%7B2%7D++-+5x+%2B++%7Bx%7D%5E%7B2%7D++%2B+10x+%2B+25+%3D+50+%5C%5C+2+%7Bx%7D%5E%7B2%7D++%2B+5x+-+25+%3D+0+%5C%5C+D+%3D+25+%2B+200+%3D+225+%3D+15+%5C%5C+x+1+%3D++%5Cfrac%7B+-+5+%2B+15%7D%7B4%7D++%3D++%5Cfrac%7B10%7D%7B4%7D++%3D+2.5+%5C%5C+x2+%3D++%5Cfrac%7B+-+5+-+15%7D%7B4%7D++%3D++-+5)
Ответ: х=2.5
<span>cos^2(п-a)+cos^2(3п/2-a)=cos²a+sin²a=cos²a+sin²a=1</span>