Вправи: 1053

1053. Виконайте дії:

1) x-1x2+ 2x-3 + x+1x2+ 4x+3.

x² + 2x – 3 = 0; D = 2² – 4 • (–3) = 16; x₁ = -2+42 = 1;

x₂ = -2-42 = –3.

x² + 4x + 3 = 0; D = 4² – 4 • 3 = 4; x₁ = -4+42 = –1;

x₂ = -4-22 = –3.

x-1x-1(x+3) + x+1x+1(x+3) = 1x+3 + 1x+3 = 2x+3.

2) 2x2- 7x2- 3x-4 – x+1x-4.

x² – 3x – 4 = 0; D = (–3)² – 4 • (–4) = 25;

x₁ = 3+52 = 4; x₂ = 3-52 = –1.

2x2- 7x-4(x+1) – x+1x-4 = 2x2- 7-(x+1)2x-4(x+1) = 2x2- 7- x2- 2x-1x-4(x+1) = x2- 2x-8x-4(x+1).

x² – 2x – 8 = 0; D = (–2)² – 4 • (–8) = 36;

x₁ = 2+62 = 4; x₂ = 2-62 = –2.

x2- 2x-8x-4(x+1) = x-4(x+2)x-4(x+1) = x+2x+1.

3) x2- x-202-x • 2x- x2x+4.

x² – x – 20 = 0; D = (–1)² – 4 • (–20) = 81;

x₁ = 1+92 = 5; x₂ = 1-92 = –4.

x-5x+4 • x(2-x)2-x(x+4) = x(x-5)1 = x² – 5x.

4) x+52x-6 : x2+ 11x+30x-3.

x² + 11x + 30 = 0; D = 11² – 4 • 30 = 1;

x₁ = -11+12 = –5; x₂ = -11-12 = –6.

x+5(x-3)2x-3x+5(x+6) = 12(x+6).