Question

oblicz równania

a)(x-3)²-(x+5)(x-5)=52

b)(x-2)²-2x=1-(3-x)(3+x)

c)(a-2)(a+2)+4=(a-2)²

d)(y+1)²-7=(y+3)(y-3)

e)4(z-1)²+(2z+3)(3-2z)=-4z+1

f)(x+1)²=(x-1)²-2(x-4)(x+1)(x+1)=(x-1)(x-1)-2x+8

możliwi jak najszybciej

Answer 1

a)(x-3)²-(x+5)(x-5)=52

x²-6x+9-x²-5x+5x-25=52

-6x=52+25-9

-6x=68   /(-6)

x=11⅓

b)(x-2)²-2x=1-(3-x)(3+x)

x²-4x+4-2x=1-(9+3x-3x-x²)

x²-6x+4= 1-9-3x+3x+x²

x²-6x+4=-8+x²

x²-6x-x²= -8-4

-6x=-12   /(-6)

x=2

c)(a-2)(a+2)+4=(a-2)²

a²+2a-2a-4+4=a²-4a+4

a²-a²+4a=4

4a=4   /4

a=1

 

d)(y+1)²-7=(y+3)(y-3)

y²-2y+1-7=y²-3y+3y-9

y²-2y-6=y²-9

y²-2y-y²=-9+6

-2y= -3    /(-2)

y= 2/3

 

e)4(z-1)²+(2z+3)(3-2z)=-4z+1

4(z²-2z+1)+6z-4z²+9-6z= -4z+1

4z²-8z+4+6z-4z²+9-6z= -4z+1

-8z+13= -4z+1

-8z+4z=1-13

-4z= -12   /(-4)

z=3

 

 

 

 

 

 

Answer 2

a)(x-3)²-(x+5)(x-5)=52

(x²-6x+9)-(x²-25)=52

x²-6x+9-x²+25=52

-6x+34=52

-6x=18

x=-3

 

b)(x-2)²-2x=1-(3-x)(3+x)

x²-4x+4-2x=1-(9-x²)

x²-4x+4-2x=1-9+x²

x²-x²-4x-2x=1-9-4

-6x=-12

6x=12

x=2

 

 

c)(a-2)(a+2)+4=(a-2)²

a²-4+4=a²-4a+4

a²-a²+4a=4-4

4a=0

a=0

 

 

d)(y+1)²-7=(y+3)(y-3)

y²+2y+1-7=y²-9

y²-y²+2y=-9-1+7

2y=-3

y=-1,5

 

 

e)4(z-1)²+(2z+3)(3-2z)=-4z+1

4(z²-2z+1)+9-4z²=-4z+1

4z²-8z+4+9-4z²=-4z+1

-4z=-12

4z=12

z=3

 

 

f)(x+1)²=(x-1)²-2(x-4)(x+1)(x+1)=(x-1)(x-1)-2x+8

x²+2x+1=x²-2x+1-2x+8+x²+x+x+1=x²-x-x+1-2x+8

x²+2x+1=x²-2x+1-2x+8+x²+x+x+1-x²+x+x-1+2x-8

x²+2x-x²+2x+2x-x²-x-x+x²-x-x-2x=-1+1+8+1-1-8

0=0

Rownanie tozsamosciowe, ma nieskonczenie wiele rozwiazan