Question

Rozwiaz i sprawdz a)y(y-1)-y^{2}=2 b)2x(2x-5)-4(x^{2}+1=1 c)3(x+2)-x(1-x)-x^{2}=18 d)x(x-3)+4(x-5)=x^{2}-2x+4 prosze o czytelne rozwiazanie

Answer 1

a)

y(y-1)-y^{2}=2

y^{2}-y-y^{2}=2

-y=2

y=-2

 

SPR:

-2(-2-1)-(-2)^{2}=2

-2(-3)-4=2

6-4=2

2=2

 

b)

2x(2x-5)-4(x^{2}+1)=1

4x^{2}-10x-4x^{2}-4=1

-10x-4=1

-10x=5

-x=0,5

x=-0,5

 

SPR:

2(-0,5)(2(-0,5)-5)-4((-0,5)^{2}+1)=1

-1(-1-5)-4(0,25+1)=1

-1(-6)-4(1,25)=1

6-5=1

1=1

 

c)

3(x+2)-x(1-x)-x^{2}=18

3x+6-x+x^{2}-x^{2}=18

2x+6=18

2x=12

x=6

 

SPR:

3(6+2)-6(1-6)-6^{2}=18

3(8)-6(-5)-36=18

24+30-36=18

18=18

 

d)

x(x-3)+4(x-5)=x^{2}-2x+4

x^{2}-3x+4x-20=x^{2}-2x+4

x^{2}+x-20=x^{2}-2x+4

x^{2}+x-20-x^{2}+2x-4=0

3x-24=0

3x=24

x=8

 

SPR:

8(8-3)+4(8-5)=8^{2}-2(8)+4

8(5)+4(3)=64-16+4

40+12=52

52=52