ПОВТОРЕННЯ І СИСТЕМАТИЗАЦІЯ » 25 (1-4)

Розв’яжіть рівняння методом заміни змінної: 1) x4 – 7x2 + 6 = 0; x2 = t; t2 – 7t + 6 = 0; t1 = 6 t2 = 1; x2 = 6 x2 = 1; x = ±√6; x = ±1. В: –√6; –1; 1; √6 2) x4 + 8x2 – 9 = 0; x2 = t; t2 + 8t – 9 = 0; t1 = –9; t2 = 1; x2 = –9; x2 = 1; ∅ x = ±1. 3) (3x + 1)4 – (3x + 1)2 – 6 = 0; (3x + 1)2 = t; t2 – t – 6 = 0; t1 = 3; t2 = –2; (3x + 1)2 = 3; (3x + 1)2 = –2; ∅ 4) (8x – 7)4 + 3(8x – 7)2 – 10 = 0 (8x – 7)2 = t; t2 + 3t – 10 = 0; t1 = –5 t2 = 2; (8x – 7)2 = –5; (8x – 7)2 = 2; ∅ 3x + 1 = √3 3x + 1 = –√3 3x = √3 – 1 3x = –√3 – 1 x = (√3- 1)/3 x = (-√3- 1)/3 8x – 7 = √2 8x – 7 = –√2 8x = 7 + √2 8x =7 – √2 x = (7+ √2)/8 x = (7- √2)/8