Question

Решите уравнение: 2(x-2)^2=8 3(x-5)^2=6 10(x-3)^2=10

Answer 1

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Answer 2

2(x - 2)(x - 2) = 8
2(x² - 4x + 4) = 8
2x² - 8x + 8 = 8
2x² - 8x = 8 - 8
2x² - 8x = 0
2x(x - 4) = 0
Произведение равно 0,когда один из множителей равен 0,значит,
2x = 0
x =0
x - 4 = 0
x = 4
Ответ: x = 0, x = 4.

3(x - 5)(x - 5) = 6
3( x² - 10x + 25) =6
3x² - 30x + 75 - 6 = 0
3x² - 30x + 69 = 0
x² - 10x + 23 = 0
D = b² - 4ac = 100 - 4 × 23 = 100 - 92 = 8
x1,2 = ( 10 +/- √8) / 2 = (10+/-2√2) / 2
x1 = 5 + √2, x2 = 5 - √2

10(x - 3)(x - 3) = 10
10( x² - 6x + 9) = 10
10x² - 60x + 90 - 10 = 0
10x² - 60x + 80 = 0
x² - 6x + 8 = 0
D = b² - 4ac = 36 - 4 × 8 = 36 - 32 = 4 = 2²
x1 = (  6 + 2) / 2 = 4
x2 = ( 6 - 2) / 2 = 2
Ответ: x1 = 4, x2 = 2.

Answer 3

Решим данное уравнение поэтапно:

1) 2(x-2)^2 = 8 Раскроем скобки: 2(x^2 - 4x + 4) = 8 Упростим: 2x^2 - 8x + 8 = 8 2x^2 - 8x = 0 Вынес