![x^{2}+\frac{1}{x^{2} }+7(x-\frac{1}{x})+10=0\\\\x-\frac{1}{x}=m\\\\(x-\frac{1}{x})^{2}=x^{2}-2*x*\frac{1}{x}+\frac{1}{x^{2} }=x^{2}-2+\frac{1}{x^{2} }\\\\x^{2}+\frac{1}{x^{2} }=m^{2}+2\\\\m^{2}+2+7m+10=0\\\\m^{2}+7m+12=0\\\\m_{1}=-3;m_{2}=-4](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D+%7D%2B7%28x-%5Cfrac%7B1%7D%7Bx%7D%29%2B10%3D0%5C%5C%5C%5Cx-%5Cfrac%7B1%7D%7Bx%7D%3Dm%5C%5C%5C%5C%28x-%5Cfrac%7B1%7D%7Bx%7D%29%5E%7B2%7D%3Dx%5E%7B2%7D-2%2Ax%2A%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D+%7D%3Dx%5E%7B2%7D-2%2B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D+%7D%5C%5C%5C%5Cx%5E%7B2%7D%2B%5Cfrac%7B1%7D%7Bx%5E%7B2%7D+%7D%3Dm%5E%7B2%7D%2B2%5C%5C%5C%5Cm%5E%7B2%7D%2B2%2B7m%2B10%3D0%5C%5C%5C%5Cm%5E%7B2%7D%2B7m%2B12%3D0%5C%5C%5C%5Cm_%7B1%7D%3D-3%3Bm_%7B2%7D%3D-4)
![1)x-\frac{1}{x}=-3\\\\x^{2}-1=-3x\\\\x^{2}+3x-1=0\\\\D=3^{2}-4*(-1)=9+4=13\\\\x_{1} =\frac{-3+\sqrt{13} }{2}\\\\x_{2}=\frac{-3-\sqrt{13} }{2}](https://tex.z-dn.net/?f=1%29x-%5Cfrac%7B1%7D%7Bx%7D%3D-3%5C%5C%5C%5Cx%5E%7B2%7D-1%3D-3x%5C%5C%5C%5Cx%5E%7B2%7D%2B3x-1%3D0%5C%5C%5C%5CD%3D3%5E%7B2%7D-4%2A%28-1%29%3D9%2B4%3D13%5C%5C%5C%5Cx_%7B1%7D+%3D%5Cfrac%7B-3%2B%5Csqrt%7B13%7D+%7D%7B2%7D%5C%5C%5C%5Cx_%7B2%7D%3D%5Cfrac%7B-3-%5Csqrt%7B13%7D+%7D%7B2%7D)
![2)x-\frac{1}{x}=-4\\\\x^{2}-1=-4x\\\\x^{2}+4x-1=0\\\\D=4^{2}-4*(-1)=16+4=20=(2\sqrt{5})^{2}\\\\x_{3}=\frac{-4+2\sqrt{5} }{2}=\sqrt{5}-2\\\\x_{4}=\frac{-4-2\sqrt{5} }{2}=-\sqrt{5}-2](https://tex.z-dn.net/?f=2%29x-%5Cfrac%7B1%7D%7Bx%7D%3D-4%5C%5C%5C%5Cx%5E%7B2%7D-1%3D-4x%5C%5C%5C%5Cx%5E%7B2%7D%2B4x-1%3D0%5C%5C%5C%5CD%3D4%5E%7B2%7D-4%2A%28-1%29%3D16%2B4%3D20%3D%282%5Csqrt%7B5%7D%29%5E%7B2%7D%5C%5C%5C%5Cx_%7B3%7D%3D%5Cfrac%7B-4%2B2%5Csqrt%7B5%7D+%7D%7B2%7D%3D%5Csqrt%7B5%7D-2%5C%5C%5C%5Cx_%7B4%7D%3D%5Cfrac%7B-4-2%5Csqrt%7B5%7D+%7D%7B2%7D%3D-%5Csqrt%7B5%7D-2)
Сумма корней :
x₁ + x₂ + x₃ + x₄ = - 3 - 4 = - 7
M²+3m-28 разложим на множители сначала найдем "нулевые" точки
m²+3m-28=0
D=9+112=121
m1=(-3-11)/2=-7
m2=(-3+11)/2=4
m²+3m-28=(m+7)(m-4) что и требовалось доказать
2. х²+6х-12х²=2х-2-х²+х-2
-11х²+6х=-х²+3х-4
-10х²+3х+4=0
D=9+160=169
х1=(-3-13)/-20=0.8
х2=(-3+13)/-20=-0.5
1/m+n-1/n =1*n/(m+n)*n-1*(m+n)/(m+n)*n =m-(m+n)/n*(m+n)=m-m-n/n*(m+n)=-n/n*(m+n)=-1/m+n
Мода - число, которое повторяется больше всего раз.
Мода данного ряда чисел равна 4, так как именно это число повторяется чаще остальных.
Мо = 4.
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Sunny Storm (Darknight)