Question

(3X-1)² + (4 X + 2)² = (5x-1) · (5x + 1)​

Answer 1

3x-1)^2+(4x+2)^2=(5x-1)•(5х+1) 9x^2-6x+1+16x^2+16x+4=25x^2+5х-5х-1

Приводим подобные, получаем:

10х=6

х=6/10

х=0,6

Answer 2

To solve the equation $(3x - 1)^2 + (4x + 2)^2 = (5x - 1)(5x + 1)$, you can follow these steps:

1. Expand both sides of the equation:

$(3x - 1)^2 + (4x + 2)^2 = (5x - 1)(5x + 1)$

Expanding the squares:

$(9x^2 - 6x + 1) + (16x^2 + 16x + 4) = 25x^2 - 1$

2. Combine like terms on both sides of the equation:

$(9x^2 - 6x + 1) + (16x^2 + 16x + 4) = 25x^2 - 1$

Combine the terms within the parentheses:

$9x^2 - 6x + 1 + 16x^2 + 16x + 4 = 25x^2 - 1$

3. Combine like terms on the left side:

$25x^2 + 10x + 5 = 25x^2 - 1$

4. Now, we can simplify further:

Subtract $25x^2$ from both sides of the equation to eliminate the quadratic terms:

$10x + 5 = -1$

5. Subtract 5 from both sides of the equation:

$10x = -1 - 5$

$10x = -6$

6. Finally, divide both sides by 10 to solve for x:

$x = \frac{-6}{10}$

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

$x = \frac{-3}{5}$

So, the solution to the equation is $x = -\frac{3}{5}$.

Answer 3

To solve the equation (3x-1)² + (4x+2)² = (5x-1) · (5x+1), you'll first need to expand and simplify both sides of the equation. Here's how to do it step by step:

1. Expand the left side of the equation: (3x-1)² + (4x+2)² = (3x-1)(3x-1) + (4x+2)(4x+2)

2. Use the distributive property to multiply the binomials: (3x-1)(3x-1) = 9x² - 6x + 1 (4x+2)(4x+2) = 16x² + 8x + 8x + 4 = 16x² + 16x + 4

3. Combine like terms on the left side: 9x² - 6x + 1 + 16x² + 16x + 4 = (5x-1)(5x+1)

4. Combine like terms on the left side further: 25x² + 10x + 5 = (5x-1)(5x+1)

5. Expand the right side of the equation: (5x-1)(5x+1) = 25x² - 1

Now, the equation becomes: 25x² + 10x + 5 = 25x² - 1

6. Subtract 25x² from both sides of the equation to eliminate the quadratic terms: 10x + 5 = -1

7. Subtract 5 from both sides of the equation: 10x = -1 - 5 10x = -6

8. Finally, divide both sides by 10 to solve for x: x = -6 / 10 x = -3/5

So, the solution to the equation is x = -3/5.