Question

решите уравнения через Дискриминант

1)Х2+2x - 7 =0

2)X2+3x-1 1/2=0

Answer 1

1) Х² + 2x - 7 = 0
D = 4 + 4*1*7 = 32
x₁ = (- 2 - 4√2)/2
x₁ = - 1 - 2√2
x₂ = (- 2 + 4√2)/2
x₂  = - 1 + 2√2

2) X² + 3x - 1(1/2)  = 0
D = 9 + 4*1*(3/2) = 15
x₁ = (- 3 - √15)/2
x₂ = (- 3 + √15)/2

Answer 2

$1) x^2+2x-7=0,\D=2^2-4bullet1bullet(-7)=4+28=32,\\x_1=frac{-2+sqrt{32}}{2}=frac{-2+4sqrt2}{2}=-1+2sqrt2,\\x_2=-1-2sqrt2.$


$2) x^2+3x-1frac{1}{2}=0 |bullet2,\2x^2+6x-3=0,\D=6^2-4bullet2bullet(-3)=36+24=60,\\x_1=frac{-6+sqrt{60}}{2bullet2}=frac{-6+2sqrt{15}}{4}=frac{-3+sqrt{15}}{2},\\x_2=frac{-3-sqrt{15}}{2}.$