Respuesta :

(x_1+x_2)=-b/a=18/3=6

x_1x_2=c/a=-21/3=-7

So

  • (x_1+x_2)²-2x_1x_2=x_1^2+x2²
  • x1²+x2²=(6)²-2(-7)=36+14=50

(x_1-x_2)²

  • x1²+x2²-2x_1x2
  • 50+14
  • 64

x_1-x_2=8

semsee45

Answer:

[tex]x{_1}^2+x{_2}^2=50[/tex]

[tex]|x_1-x_2|=8[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2-18x-21=0[/tex]

Factor to find the roots:

[tex]\implies 3(x^2-6x-7)=0[/tex]

[tex]\implies x^2-6x-7=0[/tex]

[tex]\implies x^2+x-7x-7=0[/tex]

[tex]\implies x(x+1)-7(x+1)=0[/tex]

[tex]\implies (x-7)(x+1)=0[/tex]

Therefore:

[tex]\implies (x-7)=0 \implies x=7[/tex]

[tex]\implies (x+1)=0 \implies x=-1[/tex]

Therefore, the roots of the quadratic equation are:

[tex]x = 7,\quad x = -1[/tex]

Let  [tex]x_1 = 7[/tex]

Let  [tex]x_2 = -1[/tex]

[tex]\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50[/tex]

[tex]\implies |x_1-x_2|=|7-(-1)|=8[/tex]

Otras preguntas