Х³-х=0
х(х²-1)=0
х=0
или
х²-1=0
х²=1
х=1; х=-1
ответ: -1; 0; 1
х²-24х+144=0
(х-12)²=0
х-12=0
х=12
ответ: 12
25у²-49=0
25у²=49
у²=49/25
у=7/5; у=-7/5
ответ: -7/5; 7/5
Окей.
1) x²-10x+25 = 0
a=1 b=-10 c=25
D = b²-4ac => (-10²)-4*1*25 = 100-100 = 0=0, 1 корень
x = ![\frac{-b}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D)
x₁ = ![\frac{10}{2} = 5](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B2%7D+%3D+5)
Ответ: корень 5.
2) ![\frac{1}{2}x^2 + x - 5 = 0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%5E2+%2B+x+-+5+%3D+0)
0,5x^2+x-5=0
a=0,5 b=1 c=-5
D = b²-4ac => 1²-4*0,5*(-5) = 1+10 = 11>0, 2 корня
x = ![\frac{-b+-\sqrt{D} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7BD%7D+%7D%7B2a%7D)
x₁ = ![\frac{-1-\sqrt{11} }{1} = -1 - \sqrt{11}](https://tex.z-dn.net/?f=%5Cfrac%7B-1-%5Csqrt%7B11%7D+%7D%7B1%7D+%3D+-1+-+%5Csqrt%7B11%7D)
x₂ = ![\frac{-1+\sqrt{11} }{1} = -1 + \sqrt{11}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%2B%5Csqrt%7B11%7D+%7D%7B1%7D+%3D+-1+%2B+%5Csqrt%7B11%7D)
Ответ: 1) -1 - √11; 2) -1 + √11.
A) 2a -ac² +a²c -2c =2(a -c) +(a²c -ac²) =2(a -c) +ac(a -c) =(a -c)(2 +ac)
b) 25x -10x² +x^3 =x(25 -10x +x²) =x(5 -x)² =x(5 -x)(5 -x)