Question

допоможіть будь ласка срочно дам 50 балів​

Answer 1

Ответ:

1) 2x²-3x-2 = (x-2)(2x+1);
2) 5x²-7x+2 = (x-1)(5x-2);
3) x∉R;
4) 4x²-12x+9 = (2x-3)²

Объяснение:

1) 2x²-3x-2 = 0;
D = (-3)²-4*2*(-2) = 9+16 = 25 = 5²;
x₁₂ = (3±5)/(2*2);
x₁ = (3+5)/(2*2) = 8/4 = 2; x₂ = (3-5)/(2*2) = -2/4 = -1/2;
2x²-3x-2 = 2(x-2)(x-(-1/2)) = (x-2)(2x+1);

2) 5x²-7x+2 = 0;
D = (-7)²-4*5*2 = 49-40 = 9 = 3²;
x₁₂ = (7±3)/(2*5);
x₁ = (7+3)/(2*5) = 10/10 = 1; x₂ = (7-3)/(2*5) = 4/10 = 2/5;
5x²-7x+2 = 5(x-1)(x-2/5) = (x-1)(5x-2);

3) x²-8x+20 = 0;
D = (-8)²-4*1*20 = 64-80 < 0
x∉R

4) 4x²-12x+9 = 0;
D = (-12)²-4*4*9 = 144-144 = 0;
x = 12/(2*4) = 12/8 = 3/2;
4x²-12x+9 = 4(x-3/2)(x-3/2) = (2x-3)(2x-3) = (2x-3)²