x+20y+10xy=40
x+20y-10xy=-8
(x+20y+10xy)-(x+20y-10xy)=40-(-8)
x+20y+10xy-x-20y+10xy=40+8
20xy=48
xy=2.4
x+20y+24=40
x+20y=16
y=2.4/x
x+20*2.4/x=16
x+48/x=16
(x+48/x)*x=16*x
x^2+48=16x
x^2-16x+48=0
(x-4)(x-12)=0
x1=4
x2=12
y1=2.4/4=0.6
y2=2.4/12=0.2
Проверка:
4+20*0.6+10*4*0.6=40
4+12+24=40
40=40
4+20*0.6-10*4*0.6=-8
4+12-24=-8
-8=-8
12+20*0.2+10*12*0.2=40
12+4+24=40
12+4-24=-8
x+20y+10xy=40
x+20y-10xy=-8
x+20y+10xy=40
(x+20y+10xy)-(x+20y-10xy)=40-(-8)
x+20y+10xy=40
x+20y+10xy-x-20y+10xy=40+8
x+20y+10xy=40
20xy=48
x+20y+10xy=40
xy=2.4
x+20y+24=40
xy=2.4
x+20y=16
y=2.4/x
x+20*2.4/x=16
y=2.4/x
x+48/x=16
y=2.4/x
(x+48/x)*x=16*x
y=2.4/x
x^2+48=16x
y=2.4/x
x^2-16x+48=0
y=2.4/x
(x-4)(x-12)=0
y=2.4/x
x1=4
x2=12
y1=2.4/4=0.6
y2=2.4/12=0.2
Проверка:
x1=4
y1=2.4/4=0.6
x+20y+10xy=40
4+20*0.6+10*4*0.6=40
4+12+24=40
40=40
x+20y-10xy=-8
4+20*0.6-10*4*0.6=-8
4+12-24=-8
-8=-8
x2=12
y2=2.4/12=0.2
x+20y+10xy=40
12+20*0.2+10*12*0.2=40
12+4+24=40
40=40
x+20y-10xy=-8
12+4-24=-8
-8=-8
x(3x - 0,5) = 0
x =0 3x-0,5=0
3x = 0,5
x = 0,5 / 3
x = 5 / 30
x = 1/6
Б) (4-2x)^2=3x-6
4^2 - 2*4*2x + (2x)^2 = 3x-6
16 - 16x + 4x^2 = 3x -6
4x^2 -16x - 3x +16 + 6 = 0
4x^2 - 13x + 22 = 0
(Через дискриминант)
D = b^2 - 4ac
D = (-13)^2 - 4 * 4 * 22 = 169 - 352 = -183
D < 0 => НЕТ РЕШЕНИЯ
В) 2x^3-x^2+6x-3=0 x (2x^2 - x + 6x - 3) = 0
x = 0 2x^2 + 5x - 3 = 0
D = b^2-4ac
D = 5^2 - 4 * 2 * (-3) = 25 + 24 = 49 > 0 => 2 корня
x= -b ⁺₋ √D / 2a
X₁ = (-5 + √49) / 2 * 2 = 4/4 = 1
X₂ = (-5 - √49) / 2 * 2 = -14 / 4 = - 7/2 = -3,5
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