Question

Розв'яжіть будь ласка √x=8;3x²-8+2(3-x²)=1;(2x-1)(2x+1)=x²+2;(x-3)²+(x+3)²=146;9-(0,5x-1)²=x.​

Answer 1

Ответ:

1) x = 64

2) x = ±√3

3) x = ±1

4) x = ±8

5) x = ±4√2

Пошаговое объяснение:

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1) √x = 8

(√x)² = 8²

x = 64

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2) 3x² - 8 + 2(3 - x²) = 1

3x² - 8 + 6 - 2x² = 1

3x² - 2x² = 1 + 8 - 6

x² = 3

x = ±√3

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3) (2x - 1)(2x + 1) = x² + 2

4x² - 1 = x² + 2

4x² - x² = 2 + 1

3x² = 3

x² = 3/3

x² = 1

x = ±1

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4) (x - 3)² + (x + 3)² = 146

x² - 6x + 9 + x² + 6x + 9 = 146

2x² + 18 = 146

2x² = 146 - 18

2x² = 128

x² = 128/2

x² = 64

x = ±8

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5) 9 - (0,5x - 1)² = x

9 - (0,25x² - x + 1) = x

9 - 0,25x² + x - 1 = x

-0,25x² + x - x = 1 - 9

-0,25x² = -8

x² = -8/-0,25

x² = 32

x = ±√32

x = ±√16*2

x = ±4√2

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Answer 2

Звідси можна знайти значення x:

1. √x = 8 x = 8^2 x = 64

2. 3x² - 8 + 2(3 - x²) = 1 3x² - 8 + 6 - 2x² = 1 x² - 2 = 1 x² = 3 x = ±√3

3. (2x - 1)(2x + 1) = x² + 2 4x² - 1 = x² + 2 4x² - x² = 2 + 1 3x² = 3 x² = 1 x = ±1

4. (x - 3)² + (x + 3)² = 146 x² - 6x + 9 + x² + 6x + 9 = 146 2x² + 18 = 146 2x² = 146 - 18 2x² = 128 x² = 64 x = ±8

5. 9 - (0.5x - 1)² = x 9 - 0.25x² + x - 1 = x 8 - 0.25x² = 0 0.25x² = 8 x² = 32 x = ±√32 = ±4√2

Таким чином, ми знайшли значення x для кожного з виразів:

• x = 64
• x = ±√3
• x = ±1
• x = ±8
• x = ±4√2