Question

rozwiąż równania:

(x-3) (x-3) > (x-1) (x+2) +4

(x-4) (x+4) - x^2 < 2 (x-3)

x(x-1) - (x+1)(x+1)>2

(x-2) (x-3) - (x-1) (x+1) <2

(x-3)^2 + (2x-1)^2 = (x+2) (x-2) -2 (1-2x^2) -4

3 (x-2)^2 -2 (x-3) (x+3) =12x +x^2 -42

2(x-3)^2 -1 = (2x-3) (x+3) -2x

Answer 1

(x-3) (x-3) > (x-1) (x+2) +4  /-(x-1)(x+2)+4

(x-3)(x-3)-(x-1)(x+2)-4>0

(x-3)²-1(x-1)(x+2)-4>0

11-7x-4>0

7-7x>0  /-7

-7x> -7  /: -7

x< -7/(-7)

x<1

 

(x-4) (x+4) - x^2 < 2 (x-3)  /-2(x-3)

(x-4)(x+4)-2(x-3)-x²<0

(x-4)(x+4)-1*2(x-3)-x²<0

x²-x²-2x-10<0

-2x-10<0  /+10

-2x<10  /: -2

x>10/(-2)

x> -5

 

x(x-1) - (x+1)(x+1)>2  /-2

x(x-1)-(x+1)(x+1)-2>0

x(x-1)-1(x+1)²>0

-3x-2-1>0

-3x-3>0  /+3

-3x>3  /: -3

x<3/(-3)

x< -1

 

(x-2) (x-3) - (x-1) (x+1) <2  /-2

(x-2)(x-3)-(x-1)(x+1)-2<0

(x-2)(x-3)-1*(x-1)(x+1)-2<0

7-5x-2<0

5-5x<0  /-5

-5x< -5  /: -5

x> -5/(-5)

x>1

 

(x-3)^2 + (2x-1)^2 = (x+2) (x-2) -2 (1-2x^2) -4  /-(x+2)(x-2)-2(1-2x²)-4

(x-3)²+(2x-1)²-(x+2)(x-2)+2*(1-2x²)+4=0

(x-3)²+(2x-1)²-1(x+2)(x-2)+2(1-2x²)+4=0

5x²-x²-4x²-10x+2+4+4+10=0

4x²-4x²-10x+2+4+14=0

4-10x+16=0

20-10x=0  /-20

-10x= -20  /: -10

x= -20/(-10)

x=2

 

3 (x-2)^2 -2 (x-3) (x+3) =12x +x^2 -42 po uproszczeniu:

3(x-2)²-2(x-3)(x+3)=x²+12x-42  /-x²+12x-42

3(x-2)²-2(x-3)(x+3)-x²-12x+42=0

3(x-2)²-1*2(x-3)(x+3)-x²-12x+42=0

x²-x²-12x-12x+30+42=0

30-12x-12x+42=0

30-24x+42=0

72-24x=0  /-72

-24x= -72  /: -24

x= -72/(-24)

x=3

 

2(x-3)^2 -1 = (2x-3) (x+3) -2x  /-(2x-3)(x+3)-2x

2(x-3)²-(2x-3)(x+3)+2x-1=0

2(x-3)²-1(2x-3)(x+3)+2x-1=0

2x-15x-1+27=0

27-13x-1=0

26-13x=0  /-26

-13x= -26  /: -13

x= -26/(-13)

x=2