1.Rozwiąż układ równań:
a) (y+1)²-x(4x+5)=(y+2x) (y-2x)
3x-y=1

b) (x-1)²- (y-3)²= (x-y) (x+y)
x+2/2 - y+4/3=1

c) (2x+5)² - 30= 4x² + 18x
5y-4= 7x

d) (x-2)² + (y+x) (y-x)= y(y-1)
x+2/2 - x-y/4= x+2y/4 + 1

e) (x-2)² - (y-1)²=(x-y) (x+y) + 5
2(x-y)+y²= (y-2√2) (y+2√2)

f) y+x² -8= x+(2-x)²
3x=1

g) (x-3)² - (x+5) (x-5)=2y+48
x+y/2 - x-y/2=2


h)(2x+3)² - 9y= 8x+13+4x²
x+y/3=x-y- 5/9


( / to kreska ułamkowa)




1

Odpowiedzi

Najlepsza Odpowiedź!
2009-12-21T01:36:19+01:00
A) (y+1)²-x(4x+5)=(y+2x) (y-2x)
3x-y=1

y²+2y+1-4x²-5x=y²-4x²
3x-y=1

2y-5x=-1
3x-y=1 |*2

2y-5x=-1
6x-2y=2
------------
x=1

x=1
2y-5=-1

x=1
y=-2

b)
(x-1)²- (y-3)²= (x-y) (x+y)
x+2/2 - y+4/3=1 (2/2 ? to 1 cała..;/)

x²+2x+1-y²+6y-9=x²-y²
x+1-y+4/3=1

2x+6y=8
x-y=-4/3 |*(-2)

2x+6y=8
-2x+2y=2 i 2/3
---------------
8y=9 i 5/3 |:8
y=1

2x+6=8
y=1

x=1
y=1


c)
(2x+5)² - 30= 4x² + 18x
5y-4= 7x

4x²+20x+25-30=4x²+18x
5y-7x=4

2x=5 |*7
5y-7x=4 |*2

14x=35
10y-14x=8
-----------------
10y=43|:10
y=4.3

5*4,3-7x=4
y=4.3

-7x=4-21,5 |:(-7)
y=4,3

x=2,5
y=4,3



d)
(x-2)² + (y+x) (y-x)= y(y-1)
x+2/2 - x-y/4= x+2y/4 + 1

x²-4x+4+y²-x²=y²-y
x+1-x-y/4=x+2y/4+1 |*4

-4x=-4
4x+4-4x-y=4x+2y+4

-4x=-4 |*(-1)
-4x-3y=0

4x=4
-4x-3y=0
------------
-3y=4|:(-3)
y=-4/3

-4x-3*(-4/3)=0
y=-4/3

x=1
y=-4/3



e) (x-2)² - (y-1)²=(x-y) (x+y) + 5
2(x-y)+y²= (y-2√2) (y+2√2)

x²-4x+4-y²+2y-1=x²-y²+5
2x-2y+y²=y²-8

-4x+2y=2
2x-2y=-8
----------
-2x=-6|:(-2)
x=3

-4*3+2y=2
x=3

y=7
x=3


f)
y+x² -8= x+(2-x)²
3x=1

y+x²-8=x+4-4x+x²
3x=1

y+3x=12
3x=1 |*(-1)

y+3x=12
-3x=-1
-----------
y=11

11+3x=12
y=11

x=13
y=11


g) (x-3)² - (x+5) (x-5)=2y+48
x+y/2 - x-y/2=2 |*2

x²-6x+9-x²+25=2y+48
2x+y-2x-y=4

-6x-2y=14
0=4

nie mozna rozwiazac..

h)(2x+3)² - 9y= 8x+13+4x²
x+y/3=x-y- 5/9 |*9

4x²+12x+9-9y=8x+13+4x²
9x+3y=3x-3y-5

4x-9y=4 |*(-3)
6x+6y=-5 |*2

-12x+27y=-12
12x+12y=-10
------------------
39y=-22|:39

y=0,57