Question

1) 2х^2(2 − 3х^2) − 3х^2(4 − 2х^2) = −8 2) 5х − 4/3(дробь) + 3х − 2/6(дробь) + 2х − 1/2= 3х − 2 Решите уравнения

Answer 1

Ответ:

Объяснение:

1) 2х²(2 - 3х²) - 3х²(4 - 2х²) = -8

4х² - 6х⁴ - 12х² + 6х⁴ = -8

-8х² = -8

х² = 1

х = ±√1

х = ±1

2) 5х - 4/3 + 3х - 2/6 + 2х - 1/2 - 3х + 2 = 0

7х = 4/3 + 2/6 + 1/2 - 2

7х = 1/6

х = 1/6 * 7

х = 7/6 = 1 целая 1/6

Answer 2

To solve the equations, we need to find the values of "x" that satisfy each equation. Let's solve them one by one:

1. $2x^2(2 - 3x^2) - 3x^2(4 - 2x^2) = -8$

Step 1: Distribute and simplify the terms: $2x^2 \cdot 2 - 2x^2 \cdot 3x^2 - 3x^2 \cdot 4 + 3x^2 \cdot 2x^2 = -8$

$4x^2 - 6x^4 - 12x^2 + 6x^4 = -8$

Step 2: Combine like terms: $4x^2 - 12x^2 - 6x^4 + 6x^4 = -8$

$-8x^2 = -8$

Step 3: Divide both sides by -8 to isolate x^2: $x^2 = 1$

Step 4: Take the square root of both sides (remembering both positive and negative roots): $x = \pm 1$

So, the solutions for this equation are $x = 1$ and $x = -1$.

2. $5x - \frac{4}{3} + 3x - \frac{2}{6} + 2x - \frac{1}{2} = 3x - 2$

Step 1: Combine like terms: $5x + 3x + 2x = 3x$ (Combining the x terms)

Step 2: Combine the constant terms on the left side: $- \frac{4}{3} - \frac{2}{6} - \frac{1}{2} = -2$ (Combining the constants)

Step 3: Rewrite the equation after simplification: $10x - \frac{7}{6} = 3x - 2$

Step 4: Get all the "x" terms on one side and the constant terms on the other side: $10x - 3x = -2 + \frac{7}{6}$

$7x = -\frac{5}{6}$

Step 5: Isolate "x" by dividing both sides by 7: $x = -\frac{5}{6} \div 7$

$x = -\frac{5}{42}$

So, the solution for this equation is $x = -\frac{5}{42}$.

Therefore, the solutions to the given equations are $x = 1$, $x = -1$, and $x = -\frac{5}{42}$.