Rozwiąż układy równań
a)
2(x-3)²-3(y-1)²=-3(y-x)(y+x)-(x-1)²
x+y+1=0

b)
(2x-2)²-y(4y+1)=(2x-2y)(2x+2y)
(x-3)²-(y+3)²=(x-y)(x+y)+18
c)
(y-5)²+12y=(y+3)²+x+2
x+2y=x-4y-x-2y
₋₋₋₋₋ ⁻⁻⁻⁻⁻⁻
3 4 to w ostatnim to ułamki zwykłe

2

Odpowiedzi

2009-11-26T20:46:14+01:00
A/
2(x-3)²-3(y-1)²=-3(y-x)(y+x)-(x-1)²
2(x2-9)-3(y2-1)=3y-3x+y+x-x2-1
2x2-18-3y2+3=3y-3x+y+x-x2-1
2009-11-26T21:20:43+01:00
A)
{2(x-3)²-3(y-1)²=-3(y-x)(y+x)-(x-1)²
{x+y+1=0
{2(x²-9) - 3(y²-1) =3(y²-x²)-x²+1
{x+y = -1
{2x²-18 - 3y²+ 3 = 3y² - 3x² -x² +1
{x+y= -1
{6x²-15 - 6y² = 1
{x+y =-1
{6x²-6y²=16
{x+y=-1 => x = -1 -y
6(-1-y)²-6y²=1
6(1+2y+y²)-6y²=1
6+12y+6y²-6y²=1
6+12y=1
12y=1-6
12y=-5
y=-⁵/₁₂
x - ⁵/₁₂ +1 = 0
x = ⁷/₁₂
b)
(2x-2)²-y(4y+1)=(2x-2y)(2x+2y)
(x-3)²-(y+3)²=(x-y)(x+y)+18
4x²-8x+4-4y²-y=4x²-4y²
x²-6x+9-y²-6y-9=x²-y²+18
4x²-8x-4x²+4y²-4y²=-4
x²-6x-x²-y²+y²-6y=27
-8x=-4
-6y-6x=27
x=₁/₂
-6y-3=27
-6y=30
y=-5
x=₁/₂
c)
(y-5)²+12y=(y+3)²+x+2
x+2y=x-4y-x-2y
y²-10y+25+12y=y²+6y+9+x+2
8y+x=0
y²-10y+12y-y²-6y-x=-23
x=-8y
-4y-x=-23
-4y+8y=-23
4y=-23
y=-⁴/₂₃
x=-8*(-⁴/₂₃)
x=³²/₂₃
x=1⁹/₂₃