<span>9x²-6xy+y²+15x-5y = </span>(3 х-у)(3 х-у+5)
Если a и b оба положительны, или оба отрицательны.
![5*4 ^{x} + 3*10 ^{x} = 2* 25 ^{x}](https://tex.z-dn.net/?f=5%2A4+%5E%7Bx%7D+%2B+3%2A10+%5E%7Bx%7D+%3D+2%2A+25+%5E%7Bx%7D+)
Разделим обе части на
![25 ^{x}](https://tex.z-dn.net/?f=25++%5E%7Bx%7D++)
![5*( \frac{4}{25}) ^{x} + 3*( \frac{10}{25} ) ^{x} - 2*( \frac{25}{25}) ^{x}= 0](https://tex.z-dn.net/?f=5%2A%28+%5Cfrac%7B4%7D%7B25%7D%29+%5E%7Bx%7D+%2B+3%2A%28+%5Cfrac%7B10%7D%7B25%7D+%29+%5E%7Bx%7D+-+2%2A%28+%5Cfrac%7B25%7D%7B25%7D%29+%5E%7Bx%7D%3D+0+++)
![5*( \frac{2}{5}) ^{2x} +3*( \frac{2}{5}) ^{x} - 2 = 0](https://tex.z-dn.net/?f=5%2A%28+%5Cfrac%7B2%7D%7B5%7D%29+%5E%7B2x%7D+%2B3%2A%28+%5Cfrac%7B2%7D%7B5%7D%29+%5E%7Bx%7D+-+2+%3D+0++)
Обозначим
![( \frac{2}{5}) ^{x}= m\ \textgreater \ 0](https://tex.z-dn.net/?f=%28+%5Cfrac%7B2%7D%7B5%7D%29+%5E%7Bx%7D%3D+m%5C+%5Ctextgreater+%5C++0++)
![5 m^{2} + 3m - 2 = 0](https://tex.z-dn.net/?f=5+m%5E%7B2%7D+%2B+3m+-+2+%3D+0)
D = 3² - 4*5*(-2) = 9 + 40 = 49
m₁ = (- 3 + √49)/10 = (- 3 + 7)/10 = 2/5
m₂ = (- 3 - √49)/10 = (- 3 - 7)/10 = - 1 - посторонний корень
![( \frac{2}{5} ) ^{x}= \frac{2}{5}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B2%7D%7B5%7D+%29+%5E%7Bx%7D%3D++%5Cfrac%7B2%7D%7B5%7D++)
x = 1
X + √(3x + 7) = 7
√(3x + 7) = 7 - x;
ОДЗ: 7 - x > 0; x < 7
(√(3x + 7))^2 =(x - 7)^2
3x + 7 = x^2 - 14x + 49
x^2 - 17x + 42 = 0
D = 289 - 4*1*42 = 121
x1 = (17 - 11)/2
x1 = 3
x2 = (17 + 11)/2
x2 = 14, не удовлетворяет ОДЗ
Ответ: х = 3