1) (y-4)^2=y^2-8y+16;
2) (5c-1)(5c+1)=25c^2-1;
3) (7x+a)^2=49x^2+14ax+a^2;
4) (3a+2b)(3a-2b)=9a^2-4b^2.
1.
2x⁴ - 32 = 2*(x⁴ - 16) = 2*((x²)² - 4²) = 2(x² -4)(x² +4) =
= 2(x² - 2²)(x² + 4) = 2(x-2)(x+2)(x²+4)
ответ е) 2(х-2)(х+2)(х² + 4)
2.
а) S= 6a² при а=4х - 5
S = 6*(4x-5)² = 6*((4x)² - 2*4x*5+5²) = 6*(16х²- 40х +25) = 96х² - 240х+150
б) V= a³ при а=4х-5
V=(4x-5)³ = (4x)³ - 3*(4x)² * 5 +3*4x*5² - 5³ = 64x³ - 240x² +300x - 125
№3.
87² - 174 * 67 + 67² = 87² - 2*87*67 + 67² = (87 - 67)² = 20² = 20*20 = 400
(38² - 17²)/ (47² - 361)= (38 -17)(38+17) / (47² - 19²) =
= (21 * 55) / [ (47 - 19)(47 + 19) ] =
= (21 * 55) / ( 28 * 66) = (3*5) /(4 * 6) =
= (1*5)/(4*2)=5/8 = 0,625
№4.
Система уравнений (по условию) :
{ x-y = 34 ⇔ {x= 34+y
{x² - y² = 408 ⇔ {(x-y)(x+y) = 408
(34+y - y) *(34+y + y) = 408
34 (34+2y) = 408
34 + 2y = 408 : 34
34 +2у = 12
2у= 34 - 12
2у= -22
у= -11
х =34 +( -11 ) = 23
Проверим:
23 - (-11) = 23 +11 = 34
23² - (-11)² = 529 - 121 = 408
Ответ: 23 и (-11) заданные числа.
log(2)=0,301029995664
log(4корень из 2)=0.75257498916
1. ![x^2-8x+17=0](https://tex.z-dn.net/?f=x%5E2-8x%2B17%3D0)
Дискриминант: D=64-4*17=64-68=-2<0 Корней нет
2.
Корень один х=-7
3. ![2x^2+17x+36=0](https://tex.z-dn.net/?f=2x%5E2%2B17x%2B36%3D0)
Дискриминант: D=289-4*2*36=289-288=1
![x_{1;2}=\frac{-17 \pm 1}{2*2} \ \ \ \ \ \ \ \ x_1=-4 \ \ \ \ \ x_2=-4.5](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B-17%20%5Cpm%201%7D%7B2%2A2%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D-4%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-4.5)
4. ![7x^2-3x-4=0](https://tex.z-dn.net/?f=7x%5E2-3x-4%3D0)
D=9-4*7*(-4)=9+112=121
![x_{1;2}=\frac{3 \pm 11}{2*7} \ \ \ \ \ \ \ \ x_1=1 \ \ \ \ \ x_2=-4/7](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B3%20%5Cpm%2011%7D%7B2%2A7%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D1%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-4%2F7)
5. ![9x^2+6x+1=0](https://tex.z-dn.net/?f=9x%5E2%2B6x%2B1%3D0)
D=36-36=0
![x=\frac{-6 \pm 0}{2*9}=-\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%20%5Cpm%200%7D%7B2%2A9%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
6. ![x^2=0.81](https://tex.z-dn.net/?f=x%5E2%3D0.81)
![x_{1;2}=\pm \sqrt{0.81}=\pm0.9](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cpm%20%5Csqrt%7B0.81%7D%3D%5Cpm0.9)
7. ![9x^2+5x=0](https://tex.z-dn.net/?f=9x%5E2%2B5x%3D0)
![x(9x+5)=0 \ \ \ \ \ \ \ x_1=0 \ \ \ \ \ \ \ x_2=-5/9](https://tex.z-dn.net/?f=x%289x%2B5%29%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-5%2F9)
8. ![8x^2-2x-1=0](https://tex.z-dn.net/?f=8x%5E2-2x-1%3D0)
D=4+32=36
![x_{1;2}=\frac{2 \pm 6}{2*8} \ \ \ \ \ \ \ \ x_1=0.5 \ \ \ \ \ x_2=-0.25](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B2%20%5Cpm%206%7D%7B2%2A8%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D0.5%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D-0.25)
9. ![6x^2-19x+10=0](https://tex.z-dn.net/?f=6x%5E2-19x%2B10%3D0)
D=361-4*6*10=361-240=121
![x_{1;2}=\frac{19 \pm 11}{2*6} \ \ \ \ \ \ \ \ x_1=2.5 \ \ \ \ \ x_2=2/3](https://tex.z-dn.net/?f=x_%7B1%3B2%7D%3D%5Cfrac%7B19%20%5Cpm%2011%7D%7B2%2A6%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x_1%3D2.5%20%5C%20%5C%20%5C%20%5C%20%5C%20x_2%3D2%2F3)
10. ![2x^2=-8](https://tex.z-dn.net/?f=2x%5E2%3D-8)
Корней нет, т.к. ![x^2\geq0](https://tex.z-dn.net/?f=x%5E2%5Cgeq0)
11. ![16x^2-40x+25=0](https://tex.z-dn.net/?f=16x%5E2-40x%2B25%3D0)
![(4x)^2-2*4*5x+5^2=0](https://tex.z-dn.net/?f=%284x%29%5E2-2%2A4%2A5x%2B5%5E2%3D0)
![(4x-5)^2=0](https://tex.z-dn.net/?f=%284x-5%29%5E2%3D0)
x=5/4=1.25
12. ![x^2-12x+36=0](https://tex.z-dn.net/?f=x%5E2-12x%2B36%3D0)
![x^2-2*6x+6^2=0](https://tex.z-dn.net/?f=x%5E2-2%2A6x%2B6%5E2%3D0)
![(x-6)^2=0](https://tex.z-dn.net/?f=%28x-6%29%5E2%3D0)
x=6