A)
3x^2 - 24x + 21 = 0 | : 3
x^2 - 8 + 7 = 0
x1 = 7
x2 = 1
3x^2 - 24x + 21 = 3(x-7)(x-1);
б)
5x^2 + 10x - 15 = 0 | : 5
x^2 + 2x - 3 = 0
x1 = -3
x2 = 1
5x^2 + 10x - 15 = 5(x+3)(x-1);
в)
1/6x^2 + 1/2x + 1/3 = 0 | : 1/6
x^2 + 3x + 2x = 0
x1 = -2
x2 = -1
1/6x^2 + 1/2x + 1/3 = 1/6(x+2)(x+1)
г)
x^2 - 12x + 20 = 0
x1 = 10
x2 = 2
x^2 - 12x + 20 = (x-10)(x-2);
д)
-y^2 + 16y - 15 = 0 | : (-1)
y^2 - 16y + 15 = 0
y1 = 15
y2 = 1
-y^2 + 16y - 15 = -(x-15)(x-1);
е)
-x^2 - 8x + 9 = 0 | : (-1)
x^2 + 8x - 9 = 0
x1 = -9
x2 = 1
-x^2 - 8x + 9 = -(x+9)(x-1);
ж)
2x^2 - 5x + 3 = 0
2x^2/2 - 5x + 3*2 = 0
x -> a
a^2 - 5a + 6 = 0
a1 = 3
a2 = 2
x1 = 3/2 = 1,5
x2 = 2/2 = 1
2x^2 - 5x + 3 = 2(x-1,5)(x-1);
з)
5y^2 + 2y - 3 = 0
5y^2/5 + 2y - 3*5 = 0
y -> t
t^2 + 2t - 15 = 0
t1 = -5
t2 = 3
y1 = -5/5 = -1
y2 = 3/5 = 0,6
5y^2 + 2y - 3 = 5(y+1)(y-0,6);
и)
-2x^2 + 5x + 7 = 0 | : (-1)
2x^2 - 5x - 7 = 0
2x^2/2 - 5x - 7*2 = 0
x -> a
a^2 - 5a - 14 = 0
a1 = 7
a2 = -2
x1 = 7/2 = 3,5
x2 = -2/2 = -1
-2x^2 + 5x + 7 = -2(x-3,5)(x+1);