Zadanie 8
a)
[tex]8x^{2} +6 = -4x(3-2x)\\8x^{2} +6 = -12x+8x2 \ |-8x^{2} \\6 = -12x \ |:(-12)\\x = -2[/tex]
b)
[tex]6x^{2} - 4(x+3)=2x(3x-3)\\6x^{2} -4x-12=6x^{2} -6x \ |-6x^{2} \\-4x-12=-6x \ |+4x\\-12=-2x\ |(:-2)\\x = 6[/tex]
c)
[tex](x+2)(3x-1)=(3x+1)(x-2)\\3x^{2} -x +6x -2=3x^{2} -6x+x-2\ |-3x^{2} \\5x-2=-5x-2 \ |+5x\\10x-2=-2\ |+2\\10 x = 0\\x=0[/tex]
d)
[tex](1-2x)(3x+2)=1-(6x+4)(x-1)\\3x+2-6x^{2} -4x=1-6x^{2} +6x-4x+4 \ |+6x^{2} \\-x+2=2x+5 \ |+x\\2=3x+5\ |-5\\-3=3x\ |:3\\x=-1[/tex]
Zadanie 9
[tex]15 = 2 * \frac{3}{2}(x+2) + 2*\frac{1}{2} (x-1)\\15 = 3(x+2)+(x-1)\\15 = 3x+6+x-1\ |+1\\16 = 4x \ |:4\\x = 4[/tex]
Pole prostokąta
[tex]P = \frac{3}{2}(4+2) * \frac{1}{2} (4-1)\\ (\frac{3}{2} * 6) * (\frac{1}{2}*3) =\\9 * \frac{3}{2} = \frac{27}{2} = 13\frac{1}{2}[/tex]
