Для решения используем формулы сокращённого умножения:
![(a + b)^{2}= a^{2}+ 2ab + b^{2}](https://tex.z-dn.net/?f=%28a+%2B+b%29%5E%7B2%7D%3D+a%5E%7B2%7D%2B+2ab+%2B+b%5E%7B2%7D)
![(a - b)^{2}= a^{2}- 2ab + b^{2}](https://tex.z-dn.net/?f=%28a+-+b%29%5E%7B2%7D%3D+a%5E%7B2%7D-+2ab+%2B+b%5E%7B2%7D)
![1) (\sqrt{40}+4 ) ^{2} +(\sqrt{40}-4)^{2} =(\sqrt{40})^{2} +2\sqrt{40}*4+4^{2}+ (\sqrt{40})^{2} -2\sqrt{40}*4+4^{2} =40+16+40+16=116](https://tex.z-dn.net/?f=1%29+%28%5Csqrt%7B40%7D%2B4+%29+%5E%7B2%7D+%2B%28%5Csqrt%7B40%7D-4%29%5E%7B2%7D+%3D%28%5Csqrt%7B40%7D%29%5E%7B2%7D+%2B2%5Csqrt%7B40%7D%2A4%2B4%5E%7B2%7D%2B+%28%5Csqrt%7B40%7D%29%5E%7B2%7D+-2%5Csqrt%7B40%7D%2A4%2B4%5E%7B2%7D+%3D40%2B16%2B40%2B16%3D116)
![2)(2-c)^{2}-c(c+4)=2^{2}-4c+c^{2}-c^{2} -4c=2^{2}-8c=4-8c](https://tex.z-dn.net/?f=2%29%282-c%29%5E%7B2%7D-c%28c%2B4%29%3D2%5E%7B2%7D-4c%2Bc%5E%7B2%7D-c%5E%7B2%7D+-4c%3D2%5E%7B2%7D-8c%3D4-8c)
![c=-\frac{1}{8}](https://tex.z-dn.net/?f=c%3D-%5Cfrac%7B1%7D%7B8%7D)
![4-8*(-\frac{1}{8})=4+1=5](https://tex.z-dn.net/?f=4-8%2A%28-%5Cfrac%7B1%7D%7B8%7D%29%3D4%2B1%3D5)
Y=kx+m
m=4
x=0,6
y=1,4
-1,4=0,6k+4
-0,6k=4+1,4
-0,6k=5,4|:(-0,6)
k=-9
y=-9x+4
1. D=1-(4*(-56)) = 225
X1= -(1+√(225))/2=-8
X2 =-(1-√(225))/2 = 7
или
2. По теореме Виета
x1+x2 = -b/a = -1/1= -1
x1*x2 = c/a = -56/1 = -56
X1=-8
X2 = 7
X²+8x+16 = (x+4)²
(x-1)(x+4)² - 6(x+4) = 0
(x+4)*((x-1)(x+4)-6) = 0
<u>x1 = -4</u>
x²+3x-4-6 = 0
x²+3x-10 = 0
по т.Виета корни (-5) и (2)
х2 = -5
х3 = 2