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(x² - 10x + 4)(x² - 2x - 4) < 0
Разложим на множители x² - 10x + 4
x² - 10x + 4 = 0
D = (- 10)² - 4 * 1 * 4 = 100 - 16 = 84 = (2√21)²
![x_{1}= frac{10+2 sqrt{21} }{2}=5+ sqrt{21}\\ x_{2}= frac{10-2 sqrt{21} }{2}=5- sqrt{21}\\ x^{2} -10x+4=(x-5- sqrt{21})(x-5+ sqrt{21} ) x_{1}= frac{10+2 sqrt{21} }{2}=5+ sqrt{21}\\ x_{2}= frac{10-2 sqrt{21} }{2}=5- sqrt{21}\\ x^{2} -10x+4=(x-5- sqrt{21})(x-5+ sqrt{21} )](https://tex.z-dn.net/?f=+x_%7B1%7D%3D+frac%7B10%2B2+sqrt%7B21%7D+%7D%7B2%7D%3D5%2B+sqrt%7B21%7D%5C%5C+x_%7B2%7D%3D+frac%7B10-2+sqrt%7B21%7D+%7D%7B2%7D%3D5-+sqrt%7B21%7D%5C%5C+x%5E%7B2%7D+-10x%2B4%3D%28x-5-+sqrt%7B21%7D%29%28x-5%2B+sqrt%7B21%7D+%29+++++++)
Разложим на множители x² - 2x - 4
x² - 2x - 4 = 0
D = (- 2)² - 4 * 1 * (- 4) = 4 + 16 = 20 = (2√5)²
![x_{1}= frac{2+2 sqrt{5} }{2}=1+ sqrt{5} \\ x_{2} = frac{2-2 sqrt{5} }{2}=1- sqrt{5} \\\ x^{2} -2x-4=(x-1- sqrt{5} )(x-1+ sqrt{5}) \\\(x-5- sqrt{21} )(x-5+ sqrt{21})(x-1- sqrt{5})(x-1+ sqrt{5}) textless 0 x_{1}= frac{2+2 sqrt{5} }{2}=1+ sqrt{5} \\ x_{2} = frac{2-2 sqrt{5} }{2}=1- sqrt{5} \\\ x^{2} -2x-4=(x-1- sqrt{5} )(x-1+ sqrt{5}) \\\(x-5- sqrt{21} )(x-5+ sqrt{21})(x-1- sqrt{5})(x-1+ sqrt{5}) textless 0](https://tex.z-dn.net/?f=+x_%7B1%7D%3D+frac%7B2%2B2+sqrt%7B5%7D+%7D%7B2%7D%3D1%2B+sqrt%7B5%7D+%5C%5C+x_%7B2%7D+%3D+frac%7B2-2+sqrt%7B5%7D+%7D%7B2%7D%3D1-+sqrt%7B5%7D+%5C%5C%5C+x%5E%7B2%7D+-2x-4%3D%28x-1-+sqrt%7B5%7D+%29%28x-1%2B+sqrt%7B5%7D%29+%5C%5C%5C%28x-5-+sqrt%7B21%7D+%29%28x-5%2B+sqrt%7B21%7D%29%28x-1-+sqrt%7B5%7D%29%28x-1%2B+sqrt%7B5%7D%29+textless++0++++++)
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____________₀___________₀_________₀_____________₀___________
1-√5 5-√21 1+√5 5+√21
x ∈ (1 - √5 ; 5 - √21) ∪ (1 + √5 ; 5 + √21)
Разложим на множители x² - 10x + 4
x² - 10x + 4 = 0
D = (- 10)² - 4 * 1 * 4 = 100 - 16 = 84 = (2√21)²
Разложим на множители x² - 2x - 4
x² - 2x - 4 = 0
D = (- 2)² - 4 * 1 * (- 4) = 4 + 16 = 20 = (2√5)²
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____________₀___________₀_________₀_____________₀___________
1-√5 5-√21 1+√5 5+√21
x ∈ (1 - √5 ; 5 - √21) ∪ (1 + √5 ; 5 + √21)
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