Вправи
Вправи: 634
Готова відповідь до завдання 634 з ГДЗ Алгебра 8 клас Мерзляк, Полонський 2021.
Алгебра, 8 клас · Вправи
Текстова відповідь
634. Розв’яжіть рівняння:
1) x2 – 4x + 3 = 0; a = 1, b = –4, c = 3, D = b2 – 4ac = (–4)2 – 4 • 3 = 16 – 12 = 4; D = 2; x1 = 4-22 = 1; x2 = 4+22 = 3.
Відповідь: 1; 3.
2) х2 + 2x – 3 = 0; a = 1, b = 2, c = –3,
D = b2 – 4ac = 22 – 4 • (–3) = 4 + 12 = 16; D = 4;
x1 = -2-42 = –3; x2 = -2+42 = 1.
Відповідь: –3; 1.
3) x2 + 3x – 4 = 0; a = 1, b = 3, c = –4, D = b2 – 4ac = 32 – 4 • 1 • (–4) = 9 + 16 = 25; D = 5;
x1 = -3+52 = 1; x2 = -3-52 = –4.
Відповідь: –4; 1.
4) x2 – 4x – 21 = 0; a = 1, b = –4, c = –21,
D = b2 – 4ac = (–4)2 – 4 • 1 • (–21) = 16 + 84 = 100;
D = 10; x1 = 4+102 = 7; x2 = 4-102 = –3.
Відповідь: –3; 7.
5) x2 + x – 56 = 0; a = 1, b = 1, c = –56, D = b2 – 4ac = 12 – 4 • 1 • (–56) = 1 + 224 = 225;
D = 15; x1 = -1+152 = 7; x2 = -1-152 = –8.
Відповідь: –8; 7.
6) x2 – 5x – 7 = 0; a = 1, b = –6, c = –7,
D = b2 – 4ac = (–6)2 – 4 • 1 • (–7) = 36 + 28 = 64;
D = 8; x1 = 6-82 = –1; x2 = 6+82 = 7.
Відповідь: –1; 7.
7) x2 – 8x + 12 = 0; a = 1, b = –8, c = 12,
D = b2 – 4ac = (–8)2 – 4 • 1 • 12 = 64 – 48 = 16;
D = 4; x1 = 8+42 = 6; x2 = 8-42 = 2.
Відповідь: 2; 6.
8) x2 + 7x + 6 = 0; a = 1, b = 7, c = 6,
D = b2 – 4ac = 72 – 4 • 1 • 6 = 49 – 24 = 25;
D = 4; x1 = -7+52 = –1; x2 = -7-52 = –6.
Відповідь: –6; –1.
9) –x2 + 6x + 55 = 0; x2 – 6x – 55 = 0; x = 1, b = –6, c = –55,
D = b2 – 4ac = (–6)2 – 4 • 1 • (–55) = 36 + 220 = 256;
D = 16; x1 = 6+162 = 11; x2 = 6-162 = –5.
Відповідь: –5; 11.
10) 2x2 – 3x – 2 = 0; a = 2, b = –3, c = –2, D = b2 – 4ac = (–3)2 – 4 • 2 • (–2) = 9 + 16 = 25;
D = 5; x1 = 3+54 = 2; x2 = 3-54 = –12.
Відповідь: –12; 2.
11) 2x2 – x – 6 = 0; a = 2, b = –1, c = –6,
D = b2 – 4ac = (–1)2 – 4 • 2 • (–6) = 1 + 48 = 49;
D = 7; x1 = 1+74 = 2; x2 = 1-74 = –32 = –1,5.
Відповідь: –1,5; 2.
12) 3x2 – 4x – 20 = 0; a = 3, b = –4, c = –20,
D = b2 – 4ac = (–4)2 – 4 • 3 • (–20) = 16 + 240 = 256;
D = 16; x1 = 4+166 = 206 = 103 = 313; x2 = 4-166 = –2.
Відповідь: –2; 313.
13) 10x2 – 7x – 3 = 0; a = 10, b = –7, c = –3,
D = b2 – 4ac = (–7)2 – 4 • 10 • (–3) = 49 + 120 = 169;
D = 13; x1 = 7+1320 = 1; x2 = 7-1320 = -620 = –310.
Відповідь: –310; 1.
14) –5x2 + 7x – 2 = 0; 5x2 – 7x + 2 = 0; a = 5, b = –7, c = 2, D = b2 – 4ac = (–7)2 – 4 • 5 • 2 = 49 – 40 = 9;
D = 3; x1 = 7+310 = 1; x2 = 7-310 = 0,4.
Відповідь: 0,4; 1.
15) –6x2 – 7x – 1 = 0; 6x2 + 7x + 1= 0; a = 6, b = 7, c = 1,
D = b2 – 4ac = 72 – 4 • 6 • 1 = 49 – 24 = 25; D = 5;
x1 = -4-512 = –1; x2 = -7+5-12 = -212 = –16.
Відповідь: –1; –16.
16) 3x2 – 10x + 3 = 0; a = 3, b = –10, c = 3,
D = b2 – 4ac = (–10)2 – 4 • 3 • 3 = 100 – 36 = 64;
D = 8; x1 = 10+86 = 3; x2 = 10-86 = 26 = 13.
Відповідь: 13; 3.
17) –3x2 + 7x + 6 = 0; 3x2 – 7x – 6 = 0; a = 3, b = –7, c = –6,
D = b2 – 4ac = (–7)2 – 4 • 3 • (–6) = 49 + 72 = 121;
D = 11; x1 = 7+116 = 3; x2 = 7-116 = -46 = –23.
Відповідь: –23; 3.
18) x2 – 4x + 1 = 0; a = 1, b = –4, c = 1,
D = b2 – 4ac = (–4)2 – 4 = 12 > 0; D = 12 = 4 •3 = 23; x1 = 4+ 122 = 2(2+ 3)2 = 2 + 3; x2 = 4- 122 = 2(2- 3)2 = 2 – 3.
Відповідь: 2 + 3; 2 – 3.
19) 2x2 – x – 4 = 0; a = 2, b = –1, c = –4,
D = b2 – 4ac = (–1)2 – 4 • 2 • (–4) = 1 + 32 = 33; D = 33; x1 = 1+ 334; x2 = 1- 332.
Відповідь: 1+ 334; 1- 334.
20) х2 – 8х + 20 = 0; а = 1, b = –8, с = 20,
D = b2 – 4ас = (–8)2 – 4 • 1 • 20 = 64 – 80 = –16, коренів немає.