ПОВТОРЕННЯ І СИСТЕМАТИЗАЦІЯ » 25 (5-8)

5) x – 5√x + 4 = 0 √x = t t2 – 5t + 4 = 0 t1 = 4 t2 = 1 √x = 4 √x = 1 x = 16 x = 1 6) x – 2√x – 8 = 0 √x = t t2 – 2t – 8 = 0 t1 = 4 x2 = –2 √x = 4 √x = –2 x = 16 ∅ 7) √(x-10) – 6/√(x-10) = 5 ОДЗ: х > 10; √(х-10) = t; t – 6/t – 5 = 0; (t^2- 5t-6)/t = 0; t2 – 5t – 6 = 0; t1 = 6 t2 = –1; √(x-10) = 6 √(x-10) = –1; x – 10 = 36 ∅ x = 46 8) √(5+2x) + 14/√(5+2x) = 9 ОДЗ: 5 + 2x > 0 2x > –5 x > –2,5 √(5+2x) = t; t + 14/t – 9 = 0; (t^2- 9t+14)/t = 0; t1 = 7 t2 = 2; √(5+2x) = 7; √(5+2x) = 2; 5 + 2x = 49; 5 + 2x = 4; 2x = 44; 2x = –1; x = 22. x = –1/2