Відповіді до вправ § 20 - § 26: 24.33

24.33 Спростіть вираз:

1) x3- 16xx + 40 • (x-43x2 + 11x-4 – 1616- x2) = x23x-1.

1. 3x² + 11x – 4 = 0;

D = 11² – 4 • 3 • (–4) = 169; x₁ = -11+136 = 13; x₂ = -11+136 = –4.

2. x-43x2+ 11x-4 – 1616- x2 = x-43x- 13(x+4) + 16x-4(x+4) = (x-4)2+ 16(3x-1)3x-1x+4(x-4) = x2- 8x+16+48x-163x-1x+4(x-4) = x2+ 40x3x-1x+4(x-4).

3. x3- 16xx+40 • x2+ 40x3x-1x+4(x-4) = xx-4x+4x(x+40)x+403x-1x+4(x-4) = x23x-1.

2) 1(2a-2)2 : (aa2- 2a+1 – a+2a2+ a-2) = 14.

1. a² + a – 2 = 0;

D = 1² – 4 • 1 • (–2) = 9; a₁ = -1+32 = 1; a₂ = -1-32 = –2.

2. a(a-1)2 – a+2a-1(a+2) = a(a-1)2 – 1a-1 = a-(a-1)(a-1)2 = 1(a-1)2.

3. 1(2(a-1))2 : 1(a-1)2 = (a-1)24(a-1)2 = 14.