Розвяжите уравнения

а) 3x²+13x-10=0; б) 8x²-x=0; в) 16x²=49; г) x²-2x-35=0

1)

3 х² + 13 х - 10 = 0

D = 13² - 4*3 * (-10) = 169 + 120 = 289 = 17²; D>0

х₁ = (- 13 - 17) / (2*3) = - 30/6 = - 5

х₂ = (- 13 + 17) / (2*3) = 4/6 = 2/3

2)

8 х² - х = 0

х * (8 х - 1) = 0

х₁ = 0

8 х - 1 = 0

8 х = 1

х = 1/8

х₂ = 0,125

3)

16 х² = 49

(4 х) ² - 7² = 0

(4 х - 7) (4 х + 7) = 0

4 х - 7 = 0

4 х = 7

х = 7/4

х₁ = 1,75

4 х + 7 = 0

4 х = - 7

х₂ = - 1,75

3)

х² - 2 х - 35 = 0

D = (-2) ² - 4*1 * (-35) = 4 + 140 = 144 = 12²; D>0

х₁ = (- (-2) - 12) / (2*1) = (2 - 12) / 2 = - 10/2 = - 5

х₂ = (- (-2) + 12) / (2*1) = (2 + 12) / 2 = 14/2 = 7