Question

1)x^4 - x^2=0 2)|x|=6 3)|x|=10

Answer 1

1) x⁴ - x² = 0

x²(x² - 1) = 0

x²(x - 1)(x + 1) = 0

или   x² = 0     и тогда    x₁ = 0

или   x - 1 = 0  и тогда    x₂ = 1

или   x + 1 = 0  и тогда    x₃ = -1

Ответ  : - 1 ; 0 , 1

2) | x | = 6

или   x₁ = 6     или   x₂ = -6

3) | x | = 10

или   x₁ = 10     или   x₂ = - 10

Answer 2

Відповідь:

Пояснення:

1) x⁴ - x² = 0

x²(x² - 1) = 0

x²(x - 1)(x + 1) = 0

Добуток дорівнює нулю, коли один із множників дорівнює нулю, тобто:

x² = 0 або    x - 1 = 0  або x + 1 = 0

x₁ = 0            x₂ = 1             x₃ = -1

Відповідь  : - 1 ; 0 , 1

2) | x | = 6

x =±6    

3) | x | = 10

или   x = ±10  

Answer 3

Let's solve each equation step by step:

1. x^4 - x^2 = 0

First, we can factor out common terms:

x^2(x^2 - 1) = 0

Now, we have two factors:

Factor 1: x^2 = 0 Taking the square root of both sides, we get:

x = 0

Factor 2: x^2 - 1 = 0 This is a quadratic equation. Let's solve it by factoring:

(x - 1)(x + 1) = 0

Setting each factor equal to zero:

x - 1 = 0 => x = 1 x + 1 = 0 => x = -1

Therefore, the solutions to the equation x^4 - x^2 = 0 are x = 0, x = 1, and x = -1.

2. |x| = 6

This equation represents the absolute value of x being equal to 6. The absolute value of a number is always positive, so we have two cases:

Case 1: x = 6 In this case, x equals 6.

Case 2: x = -6 In this case, x equals -6.

Therefore, the solutions to the equation |x| = 6 are x = 6 and x = -6.

3. |x| = 10

Similar to the previous equation, this equation represents the absolute value of x being equal to 10.

Case 1: x = 10 In this case, x equals 10.

Case 2: x = -10 In this case, x equals -10.

Therefore, the solutions to the equation |x| = 10 are x = 10 and x = -10.