5-11х= -2x²
2x²-11x+5=0
D=121-40=81
x<span>1=11-9/10=2/10=0.2
x2=11+9/10=20/10=2
</span>9x²<span>-24х= -16
</span>9x²-24x+16=0
k=12
D=144-144=0;D=0
x=24:18=4/3
6x²<span>-4=0
</span>6x²=4
x²=2/3
x=+-√2/3
Решаем квадратные уравнения ax² + bx + c = 0 с применением дискриминанта D = b² - 4ac x₁₂ = (-b +-√D)/2a
x² - 14x - 32 = 0
D=14² - 4*1*(-32) = 196 + 128 = 324 = 18²
x₁₂ = (14+-18)/2 = 16 -2
x₁ = 16
x₂ = -2
--------
-2x² + x + 15 = 0
D = 1 - 4*(-2)*15 = 1 + 120 = 121 = 11²
x₁₂ = (-1 +- 11)/2*(-2) = ( -1 +- 11)/(-4) = 3 -5/2
x₁ = 3
x₂ = -5/2
Решение
<span>Log3 X +logx 3 =2
x > 0, x </span>≠ 1<span>
log</span>₃ x + log₃ 3/log₃ x = 2
log₃ ² - 2log₃x + 1 = 0
log₃x = z
z² - 2z + 1 = 0
(z - 1)² = 0
z = 1
<span>log₃x = 1
</span><span>x = 3</span>
Так как
, то по теореме Виета
![x_1+x_2=p~~\Rightarrow~~ x_1=p-x_2](https://tex.z-dn.net/?f=x_1%2Bx_2%3Dp~~%5CRightarrow~~+x_1%3Dp-x_2)
![x_1x_2=-10~~\Rightarrow~~~ (p-x_2)x_2=-10](https://tex.z-dn.net/?f=x_1x_2%3D-10~~%5CRightarrow~~~+%28p-x_2%29x_2%3D-10)
И решим уравнение
в целых числах.
Делители числа 10: 1, 2, 5, 10.
![\displaystyle \left \{ {{p-x_2=1} \atop {x_2=-10}} \right.~~\Leftrightarrow~~~\left \{ {{p=-9} \atop {x_2=-10}} \right.\\ \\ \left \{ {{p-x_2=-10} \atop {x_2=1}} \right.~~\Rightarrow~~~\left \{ {{p=-9} \atop {x_2=1}} \right.\\ \\ \left \{ {{p-x_2=-1} \atop {x_2=10}} \right.~~\Rightarrow~~\left \{ {{p=9} \atop {x_2=10}} \right.\\ \left \{ {{p-x_2=10} \atop {x_2=-1}} \right.~~\Rightarrow~~\left \{ {{p=9} \atop {x_2=-1}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D1%7D+%5Catop+%7Bx_2%3D-10%7D%7D+%5Cright.~~%5CLeftrightarrow~~~%5Cleft+%5C%7B+%7B%7Bp%3D-9%7D+%5Catop+%7Bx_2%3D-10%7D%7D+%5Cright.%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D-10%7D+%5Catop+%7Bx_2%3D1%7D%7D+%5Cright.~~%5CRightarrow~~~%5Cleft+%5C%7B+%7B%7Bp%3D-9%7D+%5Catop+%7Bx_2%3D1%7D%7D+%5Cright.%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D-1%7D+%5Catop+%7Bx_2%3D10%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D9%7D+%5Catop+%7Bx_2%3D10%7D%7D+%5Cright.%5C%5C+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D10%7D+%5Catop+%7Bx_2%3D-1%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D9%7D+%5Catop+%7Bx_2%3D-1%7D%7D+%5Cright.)
![\displaystyle \left \{ {{p-x_2=2} \atop {x_2=-5}} \right.~~\Rightarrow~~\left \{ {{p=-3} \atop {x_2=-5}} \right.\\ \\\left \{ {{p-x_2=-5} \atop {x_2=2}} \right.~~\Rightarrow~~\left \{ {{p=-3} \atop {x_2=2}} \right.\\ \\ \left \{ {{p-x_2=-2} \atop {x_2=5}} \right.~~\Rightarrow~~\left \{ {{p=3} \atop {x_2=5}} \right.\\ \\ \left \{ {{p-x_2=5} \atop {x_2=-2}} \right.~~\Rightarrow~~\left \{ {{p=3} \atop {x_2=-2}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D2%7D+%5Catop+%7Bx_2%3D-5%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D-3%7D+%5Catop+%7Bx_2%3D-5%7D%7D+%5Cright.%5C%5C+%5C%5C%5Cleft+%5C%7B+%7B%7Bp-x_2%3D-5%7D+%5Catop+%7Bx_2%3D2%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D-3%7D+%5Catop+%7Bx_2%3D2%7D%7D+%5Cright.%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D-2%7D+%5Catop+%7Bx_2%3D5%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D3%7D+%5Catop+%7Bx_2%3D5%7D%7D+%5Cright.%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7Bp-x_2%3D5%7D+%5Catop+%7Bx_2%3D-2%7D%7D+%5Cright.~~%5CRightarrow~~%5Cleft+%5C%7B+%7B%7Bp%3D3%7D+%5Catop+%7Bx_2%3D-2%7D%7D+%5Cright.)
Ответ: ± 3; ± 9.