С точка пересечения, треугольник ABC равнобедренный,поэтому угол ABC=72°,тогда угол ABO=90-72=18
А) -z-3z=4
-4z=4
z = -1
b) y-4y = 1
-3y = 1
y = -1/3
5x-5+3x-4x = 4x-5
2a-15-a+6 = a - 9
1.5a+a+2.5a = 5a
6y +8 +6y = 12y+8
2 ^ (5+3X) = 0.16 * 5^(5+3X)
Есть в уравнение четвертой степени вида (х + а)(х + b)(x + c)(x + d) = m, и такое его решение, <span>где а + b = c + d, или а + с = b + d, или а + d = b + c.
В данном примере будет </span> а + с = b + d.
![(x^2-4)(x+1)(x-3)=5\\ (x-2)(x+2)(x+1)(x-3)=5\\ -2+1=2+(-3)\\ -1=-1](https://tex.z-dn.net/?f=%28x%5E2-4%29%28x%2B1%29%28x-3%29%3D5%5C%5C%0A%28x-2%29%28x%2B2%29%28x%2B1%29%28x-3%29%3D5%5C%5C%0A-2%2B1%3D2%2B%28-3%29%5C%5C%0A-1%3D-1)
Перемножим эти пари скобок, имеем:
![((x-2)(x+1))*((x+2)(x-3))=5\\ (x^2+x-2x-2)(x^2-3x+2x-6)=5\\ (x^2-x-2)(x^2-x-6)=5\\ ](https://tex.z-dn.net/?f=%28%28x-2%29%28x%2B1%29%29%2A%28%28x%2B2%29%28x-3%29%29%3D5%5C%5C%0A%28x%5E2%2Bx-2x-2%29%28x%5E2-3x%2B2x-6%29%3D5%5C%5C%0A%28x%5E2-x-2%29%28x%5E2-x-6%29%3D5%5C%5C%0A)
Введем замену:
![x^2-x-6=y](https://tex.z-dn.net/?f=x%5E2-x-6%3Dy)
, тогда
![x^2-x-2=x^2-x-6+4=y+4](https://tex.z-dn.net/?f=x%5E2-x-2%3Dx%5E2-x-6%2B4%3Dy%2B4)
<span>получим уравнение:
</span>
![(y+4)y=5\\ y^2+4y-5=0\\ D=16+20=36\\ y_1=1\\ y_2=-5](https://tex.z-dn.net/?f=%28y%2B4%29y%3D5%5C%5C%0Ay%5E2%2B4y-5%3D0%5C%5C%0AD%3D16%2B20%3D36%5C%5C%0Ay_1%3D1%5C%5C%0Ay_2%3D-5)
<span>Возвращаясь к исходной переменной, решим совокупность уравнений:</span>
![\left[\begin{array}{ccc}x^2-x-6=1\\x^2-x-6=-5\end{array}\right \ \ \ \ \ \left[\begin{array}{ccc}x^2-x-7=0\\x^2-x-1=0\end{array}\right \ \ \ \ \ \\ 1) x^2-x-7=0\\ D=1+28=29\\ x_1=\frac{1+\sqrt{29}}{2}\\ x_2=\frac{1-\sqrt{29}}{2}\\ 2) x^2-x-1=0\\ D=1+4=5\\ x_3=\frac{1+\sqrt{5}}{2}\\ x_4=\frac{1-\sqrt{5}}{2}\\ ](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5E2-x-6%3D1%5C%5Cx%5E2-x-6%3D-5%5Cend%7Barray%7D%5Cright+%5C+%5C+%5C+%5C+%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5E2-x-7%3D0%5C%5Cx%5E2-x-1%3D0%5Cend%7Barray%7D%5Cright+%5C+%5C+%5C+%5C+%5C+%5C%5C%0A1%29+x%5E2-x-7%3D0%5C%5C%0AD%3D1%2B28%3D29%5C%5C%0Ax_1%3D%5Cfrac%7B1%2B%5Csqrt%7B29%7D%7D%7B2%7D%5C%5C%0Ax_2%3D%5Cfrac%7B1-%5Csqrt%7B29%7D%7D%7B2%7D%5C%5C%0A%0A2%29+x%5E2-x-1%3D0%5C%5C%0AD%3D1%2B4%3D5%5C%5C%0Ax_3%3D%5Cfrac%7B1%2B%5Csqrt%7B5%7D%7D%7B2%7D%5C%5C%0Ax_4%3D%5Cfrac%7B1-%5Csqrt%7B5%7D%7D%7B2%7D%5C%5C%0A%0A)
x1, x2, x3 x4 - корни уравнения.
![\frac{1+\sqrt{29}}{2}*\frac{1-\sqrt{29}}{2}*\frac{1+\sqrt{5}}{2}*\frac{1-\sqrt{5}}{2}=\frac{(1-29)(1-{5})}{16}=\frac{-28*-4}{16}=7](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B%5Csqrt%7B29%7D%7D%7B2%7D%2A%5Cfrac%7B1-%5Csqrt%7B29%7D%7D%7B2%7D%2A%5Cfrac%7B1%2B%5Csqrt%7B5%7D%7D%7B2%7D%2A%5Cfrac%7B1-%5Csqrt%7B5%7D%7D%7B2%7D%3D%5Cfrac%7B%281-29%29%281-%7B5%7D%29%7D%7B16%7D%3D%5Cfrac%7B-28%2A-4%7D%7B16%7D%3D7)
ответ: 7