Question

tresc w załączniku.prosze o pomoc.potrzebuje to na jutro

Answer 1

a)2(2x-3)(x+1)-5(x-1)^2=2(x-2)(x-1)

2(2x^2+2x-3x-3)-5(x^2-2x+1)=2(x^2-x-2x+2)

4x^2+4x-6x-6-5x^2+10x-5=2x^2-2x-4x+4

-x^2+8x-11=2x^2-6x+4

-3x^2+14x-15=0

delta=196-180=16

pierwiastek z delty=4

x1=-14+16/-6=-1/3

x2=-14-16/-6=5

 

b) -x^2-3x+4>0

delta=9+16=25

pierwiastek z delty=5

x1=3+5/-2=-4

x2=3-5/-2=1

 

c)x^2-7x+12>0

delta=49-48=1

pierwiastek z delty=1

x1=7+1/2=4

x2=7-1/2=3

 

metoda podstawiania:

a) 3x-2y=0 =>    2y=3x =>  2y=3*-4     

6y-10x=4 => 3(3x)-10x=4   2y=-12/:2

                   9x-10x=4       y=-6

                   -x=4

                    x=-4

 

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

    1/2x-1/4y=4 /*4

 

     x^2+x-(x^2+4x+4)=y-3

     2x-y=4

   

     x^2+x-x^2-4x-4=y-3

     2x-y=4

 

      -3x-y=1  => y=-3x-1  =>    y=-3*3/5-1

       2x-y=4 => 2x-(-3x-1)=4  y=-9/5-1

                      2x+3x+1=4      y=-14/5

                      5x=3/:5

                      x=3/5

 

 

    

 

 

Answer 2

Rozwiaz rownania i nierownosci:
a)2(2x-3)(x+1)-5(x-1)2=2(x-2)(x-1)
2(2x²+2x-3x-3)-(5x+5)2=2(x²-x-2x+2)

4x²+4x-6x-6-10x-10=2x²-2x-4x+4

4x²-2x²+4x-6x-10x+2x+4x-6-10-4=0

2x²-6x-20=0

a=2 b=-6 c=-20

Δ=b²-4*a*c= (-6)²-4*2*(-20)=36+160=169

√Δ=14

x₁=-b-√Δ /2a = 6-14 /4= -8/4=-2     /--kreska ułamkowa

x₂=-b+√Δ /2a= 6+14 /4=  20/4=5

 

 

 

b) -x²-3x+4>0

a=-1 b=-3 c=4

Δ=b²-4*a*c= (-3)²-4*(-1)*4=9+16=25

√Δ=5

x₁=-b-√Δ /2a> 3-5 /-2 > -2/-2< 1    /-kreska ułamkowa

x₂=-b+√Δ /2a>3+5/-2> 8/-2< -4

 

 

c) x²-7x+12>0

a=1 b=-7 c=12

Δ=b²-4*a*c= (-7)²-4*1*12=49-48=1

√Δ=1

x₁=-b-√Δ /2a> 7-1 /2> 6/2> 3

x₂=-b+√Δ/2a>7+1/2 >8/2> 4

 

rozwiaz uklady rownan metoda podstawiania

a) {3x-2y=0
{6y-10x=4 /:2

 

{3x-2y=0

{3y-5x=4

 

-2y=-3:(-2)

{3y-5x=4

 

y=³/₂

3y-5x=4

3*³/₂ -5x=4

⁹/₂ -5x=4

-5x=4-⁹/₂

-5x= -½ /:(-1)

5x= ½ /: 5

x= ¹/₁₀

 

3*¹/₁₀ -2y=0

³/₁₀ -2y=0

-2y= -³/₁₀ /:(-2)

{y= ³/₂₀

{x= ¹/₁₀

 

 

b) {x(x+1)-(x+2)²=y-3
{½x - ¼y=4

 

{x²+x-(x²+4x+4)=y-3

{½x - ¼y=4

 

{x²+x-x²-4x-4=y-3

{½x - ¼y=4

 

{-3x-y=1

{½x - ¼y=4

-y=1+3x

½x - ¼y=4

½x - ¼*(1+3x)=4

½x - ¼+¾x=4

⁵/₄x= ¹⁷/₄   /:⁵/₄

x= 3⅖