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Ответы
Ответ дал:
0
2.1 (3 - √2)(5 + √2) - (√2 - 1)² = 15 - 5√2 + 3√2 - 2 - (2 - 2√2 + 1) = 10
2.2 { x - y = 4
{ 2x² - xy = 21
{ y = x - 4
{2x² - x(x - 4) = 21
2x² - x² + 4x - 21 = 0
x² + 4x - 21 = 0 D = b²-4ac = 16+84 = 100
x₁ = (-b+√D)/2a = (-4+10)/2 = 3 y₁ = x₁ - 4 = -1
x₂ = (-b -√D)/2a = -7 y₂ = x₂ - 4 = -11
Ответ: {3; -1}, {-7; -11}
2.4
![displaystyle frac{2x}{x^{2}-1}:( frac{1}{x^{2}+2x+1}- frac{1}{1-x^{2}})= \ \ = frac{2x}{(x-1)(x+1)}:( frac{1}{(x+1)^{2}}+ frac{1}{(x-1)(x+1)})= \ \ =frac{2x}{(x-1)(x+1)}: frac{x-1+x+1}{(x+1)^{2}(x-1)}= \ \ =frac{2x}{(x-1)(x+1)}* frac{(x+1)^{2}(x-1)}{2x}=x+1 displaystyle frac{2x}{x^{2}-1}:( frac{1}{x^{2}+2x+1}- frac{1}{1-x^{2}})= \ \ = frac{2x}{(x-1)(x+1)}:( frac{1}{(x+1)^{2}}+ frac{1}{(x-1)(x+1)})= \ \ =frac{2x}{(x-1)(x+1)}: frac{x-1+x+1}{(x+1)^{2}(x-1)}= \ \ =frac{2x}{(x-1)(x+1)}* frac{(x+1)^{2}(x-1)}{2x}=x+1](https://tex.z-dn.net/?f=displaystyle++frac%7B2x%7D%7Bx%5E%7B2%7D-1%7D%3A%28+frac%7B1%7D%7Bx%5E%7B2%7D%2B2x%2B1%7D-+frac%7B1%7D%7B1-x%5E%7B2%7D%7D%29%3D+%5C++%5C+%3D+frac%7B2x%7D%7B%28x-1%29%28x%2B1%29%7D%3A%28+frac%7B1%7D%7B%28x%2B1%29%5E%7B2%7D%7D%2B+frac%7B1%7D%7B%28x-1%29%28x%2B1%29%7D%29%3D+%5C++%5C+%3Dfrac%7B2x%7D%7B%28x-1%29%28x%2B1%29%7D%3A+frac%7Bx-1%2Bx%2B1%7D%7B%28x%2B1%29%5E%7B2%7D%28x-1%29%7D%3D+%5C++%5C+%3Dfrac%7B2x%7D%7B%28x-1%29%28x%2B1%29%7D%2A+frac%7B%28x%2B1%29%5E%7B2%7D%28x-1%29%7D%7B2x%7D%3Dx%2B1+)
2.2 { x - y = 4
{ 2x² - xy = 21
{ y = x - 4
{2x² - x(x - 4) = 21
2x² - x² + 4x - 21 = 0
x² + 4x - 21 = 0 D = b²-4ac = 16+84 = 100
x₁ = (-b+√D)/2a = (-4+10)/2 = 3 y₁ = x₁ - 4 = -1
x₂ = (-b -√D)/2a = -7 y₂ = x₂ - 4 = -11
Ответ: {3; -1}, {-7; -11}
2.4
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