Question

Помогите решить пожалуйста

Answer 1

1. x²-4x+3=0

x²-x-3x+3 = 0

x * (x-1) -3 (x-1) = 0

(x-1) * (x-3) = 0

x-1 = 0

x-3 = 0

x = 1

x = 3

x₁ = 1

x₂ = 3

2. 3x² + 5x - 2 = 0

3x² + 6x - x - 2 = 0

3x * (x+2) - (x+2) = 0

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

x + 2 = 0

3x - 1 = 0

x = -2

x = $frac{1}{3}$

x₁ = -2

x₂ = $frac{1}{3}$

3. x² + 15x + 60 = 0

x = $frac{-15+-sqrt{15^{2}-4*1*60 } }{2*1}$

x = $frac{-15+-sqrt{225-240} }{2}$

x = $frac{-15+-sqrt{-15} }{2}$

x ∉ R

4. 8x² - 13x + 5 = 0

8x² - 5x - 8x + 5 = 0

x * (8x-5) - (8x-5) = 0

(8x-5) * (x-1) = 0

8x - 5 = 0

x - 1 = 0

x = $frac{5}{8}$

x = 1

x₁ = $frac{5}{8}$

x₂ = 1

Answer 2

$1); ; x^2-4x+3=0; ; ,; ; x_1=1; ,; x_2=3; ; (teorema; Vieta)\\2); ; 3x^2+5x-2=0; ,; ; D=49; ,; ; x_1=-2; ,; x_2=frac{1}{3}\\3); ; x^2+15x+60=0; ,; ; D=-15<0; ; to ; ; xin varnothing \\4); ; 8x^2-13x+5=0; ,; ; D=9; ,; ; x_1=frac{5}{8}; ,; x_2=1\\5); ; 2x^2-5x=0; ,; ; x(2x-5)=0; ,; ; x_1=0; ,; x_2=2,5\\6); ; x^2-2x-15=0; ,; ; x_1=-3; ,; x_2=5; ; (teorema; Vieta)\\7); ; 4x^2+60x-400=0; ,; x^2+15x-100=0; ,; D=625; ,; x_1=-20,; x_2=5$

$8); ; 3x^2+2x-8=0; ,; ; D/4=25; ,; ; x_1=-2; ,; x_2=frac{4}{3}=1frac{1}{3} \\9); ; 3x^2-12x+12=0; ,; x^2-4x+4=0; ,; (x-2)^2=0; ,; x=2$