Вправи: 177

177. Доведіть тотожність:

1) 16(a-2)4 : (1(a-2)2 – 2a2- 4 + 1(a+2)2) – 8a(a-2)2 = 1.

1. 1\(a+2)2(a-2)2 – 2\a-2(a+2)a2- 4 + 1\(a-2)2(a+2)2 = (a-2)2- 2a-2a+2+ (a-2)2(a-2)2(a+2)2 = (a+2-(a-2)2(a-2)2(a+2)2=(a+2-a+2)2(a-2)2(a+2)2 = 42(a-2)2(a+2)2 = 16(a-2)2(a+2)2;

2. 16(a-2)4 : 16(a-2)2(a+2)2 = 16 • (a-2)2(a+2)2 (a-2)4 • 16 = (a+2)2(a-2)2;

3. (a+2)2(a-2)2 – 8a(a-2)2 = a2+ 4a+4-8a(a+2)2 = a2- 4a+4(a-2)2 = (a-2)2(a-2)2 = 1.

2) a+11a+9 – (a+5a2- 81 + a+7a2- 18a+81) : (a+3a-9) = 1.

1. a+5\a-9a-9(a+9) + a+ 7\a+9(a-9)2 = (a-9a+5+ (a+9)(a+7)(a-9)2(a+9) = a2+ 5a-9a-45+a2+ 9a+7a+63(a-9)2 (a+9) = 2a2+ 12a+18(a-9)2(a+9) = 2a2+ 12a+18(a-9 )2(a+9) = 2(a2+ 6a+9)(a-9)2(a+9) : (a+3a-9)² = 2(a+3)2 • (a-9)2(a-9)2a+9 • (a+3)2 = 2a+ 9;

3. a+11a+ 9 – 2a+9 = a+ 11-2a+ 9 = a+9a+9 = 1.