Question

Z rozwiązywania równiań kwadratowych

x(x+1)²-(x+2)³=-10x-3x²-8=

x²-5x+9=63-(x-3)(x+3)=

Answer 1

1.

x(x+1)^2 -(x+2)^3 = -10x -3x^2 -8

x(x^2 + 2x +1) -(x^3 +6x^2 +12x^2 +8) =-10-3x^2-8

x^3 +2x^2 +x -x^3-6x^2 -12x -8 =-10x-3x^2 -8

X^3 +2x^2 +x -x^3 -6x^2 -12x -8 +10x +3x^2 +8 =0

2x^2 -6x^2 +3x^2 +x -12x +10x =0

-x^2 -x =0

-x(x+1) =0

x =0, lub

x+1 =0

x =-1

 

{X1 =0]

{X2 =-1}

 

2.

x^2 -5x +9 =63 -(x-3)(x+3)

x^2 -5x +9 =63 -(x^2 -9)

x^2 -5x +9 =63 -x^2 +9

x^2 +x^2 -5x -63 =0

2x^2 -5x -63 =0

D =25 +504 =529

VD =23

X1 =(5-23):4 =-4,5

X2 =(5+23):4 =7

 

{X1 = -4,5}

{X2 =7}