1)![(x+4)^{2}=4x^{2}+5](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%3D4x%5E%7B2%7D%2B5%20)
<var> </var> ![x^{2}+8x+16=4x^{2}+5](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%2B8x%2B16%3D4x%5E%7B2%7D%2B5%20)
<var> </var> ![-3x^{2}+8x+11=0](https://tex.z-dn.net/?f=%20-3x%5E%7B2%7D%2B8x%2B11%3D0%20)
<var> D=64+132=196 </var>
![x_{1}=\frac{8+\sqrt{196}}{6}=\frac{22}{6}=3\frac{4}{6}=3\frac{2}{3}](https://tex.z-dn.net/?f=%20x_%7B1%7D%3D%5Cfrac%7B8%2B%5Csqrt%7B196%7D%7D%7B6%7D%3D%5Cfrac%7B22%7D%7B6%7D%3D3%5Cfrac%7B4%7D%7B6%7D%3D3%5Cfrac%7B2%7D%7B3%7D%20)
<var> </var> ![x_{2}=\frac{8-\sqrt{196}}{6}=\frac{-6}{6}=-1](https://tex.z-dn.net/?f=%20x_%7B2%7D%3D%5Cfrac%7B8-%5Csqrt%7B196%7D%7D%7B6%7D%3D%5Cfrac%7B-6%7D%7B6%7D%3D-1)
2)![9x(4x-1)=3x-1](https://tex.z-dn.net/?f=9x%284x-1%29%3D3x-1%20)
<var> </var>
<var> </var>
<var>D=144-144=0 </var>
![x_{1}=\frac{12}{2*36}=\frac{12}{72}=\frac{1}{6}](https://tex.z-dn.net/?f=%20x_%7B1%7D%3D%5Cfrac%7B12%7D%7B2%2A36%7D%3D%5Cfrac%7B12%7D%7B72%7D%3D%5Cfrac%7B1%7D%7B6%7D%20)
3)![0,09-4x^{2}=1,6x](https://tex.z-dn.net/?f=0%2C09-4x%5E%7B2%7D%3D1%2C6x%20)
<var> </var> ![-4x^{2}-1,6x+0,09=0](https://tex.z-dn.net/?f=%20-4x%5E%7B2%7D-1%2C6x%2B0%2C09%3D0%20)
<var> D=2,56+1,44=4</var>
<var> </var> ![x_{1}=\frac{1,6+\sqrt{4}}{-8}=\frac{3,6}{-8}=-0,45](https://tex.z-dn.net/?f=%20x_%7B1%7D%3D%5Cfrac%7B1%2C6%2B%5Csqrt%7B4%7D%7D%7B-8%7D%3D%5Cfrac%7B3%2C6%7D%7B-8%7D%3D-0%2C45%20)
<var> </var> ![x_{2}=\frac{1,6-\sqrt{4}}{-8}=\frac{-0,4}{-8}=0,05](https://tex.z-dn.net/?f=%20x_%7B2%7D%3D%5Cfrac%7B1%2C6-%5Csqrt%7B4%7D%7D%7B-8%7D%3D%5Cfrac%7B-0%2C4%7D%7B-8%7D%3D0%2C05)
4)
<var> </var>
<var> </var>
<var>D=0,16+5,6=5,76 </var>
<var> </var> ![x_{2}=\frac{-0,4+\sqrt{5,76}}{0,2}=\frac{-0,4+2,4}{0,2}=\frac{2}{0,2}=10](https://tex.z-dn.net/?f=%20x_%7B2%7D%3D%5Cfrac%7B-0%2C4%2B%5Csqrt%7B5%2C76%7D%7D%7B0%2C2%7D%3D%5Cfrac%7B-0%2C4%2B2%2C4%7D%7B0%2C2%7D%3D%5Cfrac%7B2%7D%7B0%2C2%7D%3D10)
5) ![(x-4)(4x-3)+3=0](https://tex.z-dn.net/?f=%28x-4%29%284x-3%29%2B3%3D0%20%20)
![4x^{2}-16x-3x+12+3=0](https://tex.z-dn.net/?f=%204x%5E%7B2%7D-16x-3x%2B12%2B3%3D0%20%20)
![4x^{2}-19x+15=0](https://tex.z-dn.net/?f=%204x%5E%7B2%7D-19x%2B15%3D0%20)
<var> D=361-240=121 </var>
![x_{1}=\frac{19+\sqrt{121}}{8}=\frac{30}{8}=\frac{15}{4}=3\frac{3}{4}](https://tex.z-dn.net/?f=%20x_%7B1%7D%3D%5Cfrac%7B19%2B%5Csqrt%7B121%7D%7D%7B8%7D%3D%5Cfrac%7B30%7D%7B8%7D%3D%5Cfrac%7B15%7D%7B4%7D%3D3%5Cfrac%7B3%7D%7B4%7D%20%20)
![x_{2}=\frac{19-\sqrt{121}}{8}=\frac{8}{8}=1](https://tex.z-dn.net/?f=%20%20x_%7B2%7D%3D%5Cfrac%7B19-%5Csqrt%7B121%7D%7D%7B8%7D%3D%5Cfrac%7B8%7D%7B8%7D%3D1)
6)![(x+5)^{2}+(x-2)^{2}+(x-7)(x+7)=11x+80](https://tex.z-dn.net/?f=%28x%2B5%29%5E%7B2%7D%2B%28x-2%29%5E%7B2%7D%2B%28x-7%29%28x%2B7%29%3D11x%2B80%20)
<var> </var>
<var> </var>
<var>D=25+1200=1225 </var>
<var> </var>
![x_{2}=\frac{5-\sqrt{1225}}{6}=\frac{-30}{6}=-6](https://tex.z-dn.net/?f=%20x_%7B2%7D%3D%5Cfrac%7B5-%5Csqrt%7B1225%7D%7D%7B6%7D%3D%5Cfrac%7B-30%7D%7B6%7D%3D-6)
F(x)=-x^2+2x+3
x₁=-1
x₂=3
Таблица и график во вложении
Ответ:
Объяснение:
1)
a) 3a²/b:b/b³=3a²/b*b³/b=3a²b³/b²=3a²b
b) -2x²/y :6x³/b²= -2x²/y*b²/6x³=-b²/3xy
B)9m/14n: 4m²/21n²=9m/14n*21n/4m²=(9*3n)/(2*4m)=27n/8m=3,375n/m
G) 12x²:6x/c=12x²*c/6x=2cx
2.
a) (x+y²)/(a-3b) : (x²-y²)/(2a-6b)=(x+y²)/(a-3b) * 2(a-3b)/(x²-y²)=2(x+y²)/(x²-y²)
b) (y-8)/(x²-4) : (2y-16)/(3x-6)=(y-8)/(x²-4)*(3x-6)/2(y-8)=3(x-2)/2(x-2)(x+2)= =3/2(x+2)
B) (c²-9)/(c²+6c+9) : (3-c)/(c+3)=(c²-9/(c+3)²* (c+3)/(3-c)= =(c-3)(c+3)/(c+3) *(-1/(c-3)=-1
Х²+ 3х-4 = x²+ 4x - x -4 = x(x+4) + (-x-4) =
= x(x+4) - (x+4) = (x-1)(x+4)
x²-8x+15 = x²- 5x-3x - 5*(-3) =
= (x²-3x) + (-5x - 5(-3))=
= x(x-3) - 5(x-3)= (x-5)(x-3)
x²+8x+12= x²+6x+2x+6*2 =
= (x²+6x) + (2x+6*2) =
=x(x+6) + 2(x+6) =(x+2)(x+6)