Вправи: 893

893. Розв’яжіть рівняння:

1) x² – 4x – 32 = 0; a = 1, b = 4, c = –32; D = 16 + 128 = 144;

D = 12; x₁ = 4+122 = 8; x₂ = 4-122 = –4.

2) x² – 10x + 21 = 0; D₁ = 25 – 24 = 1;

D2 = 2; x₁ = 5 + 2 = 7; x₂ = 5 – 2 = 3.

3) 6x² – 5x + 1 = 0; D = 25 – 24 = 1; D = 1; x₁ = 5+112 = 12;

x₂ = 5-112 = 412 = 13.

4) 8x² + 2x – 3 = 0; D₁ = 1 + 24 = 25;

D1 = 5; x₁ = -1+58 = 12; x₂ = -1-58 = -68 = –34.

5) x² + 6x – 15 = 0; D₁ = 9 + 15 = 24; D1 = 26;

x₁ = –3 + 26; x₂ = –3 – 26.

6) 3x² – x – 5 = 0; D = 1 + 60 = 61; D = 61;

x₁ = 1+ 616; x₂ = 1- 616.

7) 4x² + 28x + 49 = 0; D₁ = 14² – 4 • 49 = 196 – 196 = 0;

x = -144 = –72 = –3,5; x = –3,5.

8) x² – 16x + 71 = 0; D₁ = 64 – 71 = –7 < 0; коренів немає.