96 баллов(3 задания).1)Найти сумму корней уравнения:
![(4-x)^2+(x-4)(x^2-2x-2)=0 (4-x)^2+(x-4)(x^2-2x-2)=0](https://tex.z-dn.net/?f=%284-x%29%5E2%2B%28x-4%29%28x%5E2-2x-2%29%3D0)
2)Найти произведение корней уравнение:
![3x^4+14x^2(x-3)-5(x-3)^2=0 3x^4+14x^2(x-3)-5(x-3)^2=0](https://tex.z-dn.net/?f=3x%5E4%2B14x%5E2%28x-3%29-5%28x-3%29%5E2%3D0)
3)Вычислите
Ответы
Ответ дал:
0
1)
![(4-x)^2+(x-4)(x^2-2x-2)=0\x^2-8x+16+x^3-6x^2+6x+8=0\x^3-5x^2-2x+24=0\(x+2)(x^2-7x+12)=0\(x+2)(x-3)(x-4)=0\\-2+3+4=5 (4-x)^2+(x-4)(x^2-2x-2)=0\x^2-8x+16+x^3-6x^2+6x+8=0\x^3-5x^2-2x+24=0\(x+2)(x^2-7x+12)=0\(x+2)(x-3)(x-4)=0\\-2+3+4=5](https://tex.z-dn.net/?f=%284-x%29%5E2%2B%28x-4%29%28x%5E2-2x-2%29%3D0%5Cx%5E2-8x%2B16%2Bx%5E3-6x%5E2%2B6x%2B8%3D0%5Cx%5E3-5x%5E2-2x%2B24%3D0%5C%28x%2B2%29%28x%5E2-7x%2B12%29%3D0%5C%28x%2B2%29%28x-3%29%28x-4%29%3D0%5C%5C-2%2B3%2B4%3D5)
2)
![3x^4+14x^2(x-3)-5(x-3)^2=0\3x^4+14x^3-42x^2-5x^2+30x-45=0\3x^4+14x^3-47x^2+30x-45=0\(3x^2-x+3)(x^2+5x-15)=0 3x^4+14x^2(x-3)-5(x-3)^2=0\3x^4+14x^3-42x^2-5x^2+30x-45=0\3x^4+14x^3-47x^2+30x-45=0\(3x^2-x+3)(x^2+5x-15)=0](https://tex.z-dn.net/?f=3x%5E4%2B14x%5E2%28x-3%29-5%28x-3%29%5E2%3D0%5C3x%5E4%2B14x%5E3-42x%5E2-5x%5E2%2B30x-45%3D0%5C3x%5E4%2B14x%5E3-47x%5E2%2B30x-45%3D0%5C%283x%5E2-x%2B3%29%28x%5E2%2B5x-15%29%3D0)
По формулам Виета:
1*(-15)=-15
3)
![55+14sqrt6=49+14sqrt6+6=(7+sqrt6)^2\{36over(7+sqrt6)-7}=6sqrt6 55+14sqrt6=49+14sqrt6+6=(7+sqrt6)^2\{36over(7+sqrt6)-7}=6sqrt6](https://tex.z-dn.net/?f=55%2B14sqrt6%3D49%2B14sqrt6%2B6%3D%287%2Bsqrt6%29%5E2%5C%7B36over%287%2Bsqrt6%29-7%7D%3D6sqrt6)
2)
По формулам Виета:
1*(-15)=-15
3)
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