Вправи: 942

942. Спростіть вираз:

1) (x-12x2+ 3x+1 – 1x2- 1) : x-4x3- x = x22x+1.

1. 2x² + 3x + 1 = 0; D = 3² – 4 • 1 • 1 = 1;

x₁ = -3+14 = –12; x₂ = -3-14 = –1.

2. x-12x+1(x+ 12) – 1x-1(x+1) = (x-1)2- (2x+1)x+12x+1(x-1) = x2- 2x+1-2x-1x+12x+1(x-1) = x2- 4xx+12x+1(x-1).

3. x2- 4xx+12x+1(x-1) : x-4x3- x = xx-4x(x2- 1)x2- 12x+1(x-4) = x22x+1.

2) (3b – 9)² • (bb2- 6b+ 9 – b+2b2- b-6) = 27.

1. b² – b – 6 = 0; D = 1² – 4 • (–6) = 25;

b₁ = 1+52 = 3; b₂ = 1-52 = –2.

2. b(b-3)2 – b+2b+2(b-3) = b(b-3)2 – 1b-3 = b-(b-3)(b-3)2 = 3(b-3)2.

3. (3(b – 3))² • 3(b-3)2 = 9(b-3)2 • 3(b-3)2 = 27.