Х² - 17x +13 =0
D=(-17) ² -4*1*13 = 289- 52= 237
Корни уравнения:
x₁ = (17 - √237)/2
x₂ = (17+√237) /2
Сумма корней:
(17 -√237)/2 + (17+√237)/2 = (17-√237+17 +√237 ) /2 = 34/2 = 17
Произведение корней:
(17-√237) /2 * (17+√237)/2 = ((17-√237)(17+√237) ) / (2*2)=
= (17² - (√237)²) /4 = (289-237)/4 = 52/4= 13
<span>1)x^2-100x=0
х(х-100)=0
х=0
х-100=0
х=100
2)9/25(дробь)x^3-x=0
х(9/25х</span>²-1)=0
<span>х=0
(3/5х-1)(</span>3/5х+1)=0
3/5х=1
х=5/3
3/5х+1=0
х=-5/3
<span>3)25y^2+20y+4=0
(5у+2)</span>²=0
<span>5у+2=0
5у=-2
у=-2/5
4)36x^2+25=60x
36х</span>²-60х+25=0
<span>(6х-5)</span>²=0
<span>6х-5=0
6х=5
х=5/6
5)x^4-x^2=0
х</span>²(х²-1)=0
<span>х</span>²=0
<span>х=0
(х-1)(х+1)=0
х=1
х=-1
6)x^5-49x^3=0
х</span>³(х²-7)=0
<span>х</span>³=0
<span>х=0
х</span>²-7=0
<span>х</span>²=7
<span>х=</span>√7
<span>х=-</span>√7<span>
7)x^3+2x^2-9x-18=0
х</span>²(х+2)-9(х+2)=0
<span>(х+2)(х</span>²-9)=0
<span>х+2=0
х=-2
(х-3)(х+3)=0
х=3
х=-3
8)y^3-3y^2-4y+12=0
у</span>²(у-3)-4(у-3)=0
(у²-4)(у-3)=0
(у-2)(у+2)(у-3)=0
у=2
у=-2
у=3
<span>ctg (2x/3+пи/5)=корень из 3
</span>2x/3+пи/5=пи/6+пин
2x/3=пи/6-пи/5+пин
2x/3=11пи/30+пин
х=11пи/45+2пин/3
2.
3(x-1)-(9x-4)-3(x+3)-(2x+17)=
=3x-3-9x+4-3x-9-2x-17=
=3x-9x-3x-2x-3+4-9-17=
= -11x-25
если
![x = - 12 \frac{1}{7}](https://tex.z-dn.net/?f=x+%3D++-+12+%5Cfrac%7B1%7D%7B7%7D+)
![(- 11) \times ( - 12 \frac{1}{7}) - 25 =](https://tex.z-dn.net/?f=+%28-+11%29+%5Ctimes+%28+-+12+%5Cfrac%7B1%7D%7B7%7D%29++-+25+%3D+)
![( - \frac{11}{1} ) \times ( - \frac{84}{7} ) - 25 = \frac{924}{77} - 25 =](https://tex.z-dn.net/?f=%28+-++%5Cfrac%7B11%7D%7B1%7D+%29+%5Ctimes+%28+-++%5Cfrac%7B84%7D%7B7%7D+%29+-+25+%3D++%5Cfrac%7B924%7D%7B77%7D++-+25+%3D+)
![12 - 25 = - 13](https://tex.z-dn.net/?f=12+-+25+%3D++-+13)