12*(-3/4)-3(5/6)=-9-2,5=-11,5
a)5a+7b-2a-8b=3a-b
b) 3(4x+2) - 5= 12x+6-5=12x+1
c) 20b-(b-3)+(3b-10)=20b-b+3+3b-10=22b-7
Необходимо узнать, при каком икс значение функции
![y=-5x^2-4x+7](https://tex.z-dn.net/?f=y%3D-5x%5E2-4x%2B7)
равно шести. Приравниваем:
![-5x^2-4x+7=6](https://tex.z-dn.net/?f=-5x%5E2-4x%2B7%3D6)
; теперь решаем:
![5x^2+4x-1=0\\D=k^2-ac=4-5*(-1)=4+5=9\\x_{1,2}=\frac{-kб\sqrt{D}}{a}=\frac{-2б\sqrt{9}}{5}\to\left[\begin{array}{ccc}x_1=-1\\x_2=0,2\end{array}\right](https://tex.z-dn.net/?f=5x%5E2%2B4x-1%3D0%5C%5CD%3Dk%5E2-ac%3D4-5%2A%28-1%29%3D4%2B5%3D9%5C%5Cx_%7B1%2C2%7D%3D%5Cfrac%7B-k%D0%B1%5Csqrt%7BD%7D%7D%7Ba%7D%3D%5Cfrac%7B-2%D0%B1%5Csqrt%7B9%7D%7D%7B5%7D%5Cto%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_1%3D-1%5C%5Cx_2%3D0%2C2%5Cend%7Barray%7D%5Cright)
<span>(x+6)/(x-6) * (x-4)^2/(x+4)^2 + (x-6)/(x+6) * (x+9)^2/(x-9)^2 = 2* (x^2+36)/(x^2-36)</span>
<span>((x+6)(x-4)^2)/((x-6)(x+4)^2) + ((x-6)(x+9)^2)/((x+6)(x-9)^2=2*(x^2+36)/(x^2-36)</span>
<span>((x+6)^2(x-4)^2(x-9)^2)/((x-6)(x+4)^2(x+6)(x-9)^2) + </span>
<span>+((x-6)^2(x+9)^2(x+4)^2)/((x+6)(x-9)^2(x-6)(x+4)^2)=2*(x^2+36)/(x^2-36)</span>
<span>((x^2+12x+36)(x^2-8x+16)(x^2-18x+81) +(x^2-12x+36)(x^2+18x+81)(x^2+8x+16))/</span>
<span>/((x-6)(x+4^2(x+6)(x-9)^2) =2*(x^2+36)/(x^2-36)</span>
<span>((x^6-18x^5+4x^5-72x^4+81x^4+44x^4+792x^3+324x^3-96x^3+576x^2-3564x^2+1728x^2-10368x-7776x+46656)+(x^6+8x^5+6x^5+48x^4+16x^4-99x^4-792x^3+96x^3-324x^3+2916x^2-1584x^2-2592x^2+23328x-5184x+46656))/((x-6)(x+4)^2(x+6)(x-9)^2) =2*(x^2+36)/(x^2-36)</span>
<span>((2x^6-70x^4-2520x^2+93312))/((x-6)(x+4)^2(x+6)(x-9)^2) =2*(x^2+36)/(x^2-36)</span>
<span>(x^2+36)((2x^4-142x^2+2592)/((x-6)(x+4)^2(x+6)(x-9)^2)-2*(x^2+36)/(x^2-36))=0</span>
<span>а) x^2+36=0 => x^2=-36 - нет решений</span>
б) ((2x^4-142x^2+2592)/((x-6)(x+4)^2(x+6)(x-9)^2)-2*(x^2+36)/(x^2-36))=0
((2x^4-142x^2+2592)-2(x+4)^2(x-9)^2)/((x-6)(x+4)^2(x+6)(x-9)^2)=0
((2x^4-142x^2+2592)-2(x+4)^2(x-9)^2)=0
2x^4-2x^4+20x^3+94x^2+142x^2-720x-2592+2592=0
20x^3-48x^2-720x=0
x*(5x^2-12x-180)=0
1) x=0
2) 5x^2-12x-180=0
D=3744
X1=(6-sqrt(936))/5
x2=(6+sqrt(936))/5
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