Question

(5x-4)^2 - (3x-2 ) ( 3x+2 )= 2x(8x-5 )

Answer 1

Ответ:

25x^2 - 40x + 16 - (9x^2 - 4) = 16x^2 - 10x

25x^2 - 40x + 16 - 9x^2 + 4 = 16x^2 - 10x

25x^2 - 40x  - 9x^2 - 16x^2 + 10x = -20

16x^2 - 30x - 16x^2 = -20

-30x = -20

x = 20/30

х = 2/3

Объяснение:

Answer 2

To solve the equation (5x-4)^2 - (3x-2)(3x+2) = 2x(8x-5), follow these steps:

Step 1: Expand and simplify both sides of the equation.

Left side: (5x-4)^2 - (3x-2)(3x+2) = (5x-4)(5x-4) - (3x-2)(3x+2) = 25x^2 - 20x - 20x + 16 - (9x^2 - 4) = 25x^2 - 40x + 16 - 9x^2 + 4

Right side: 2x(8x-5) = 16x^2 - 10x

So, the equation becomes: 25x^2 - 40x + 16 - 9x^2 + 4 = 16x^2 - 10x

Step 2: Rearrange the equation and simplify:

Combine like terms on both sides: (25x^2 - 9x^2) - 40x + 16 + 4 - 16x^2 + 10x = 0

Simplify further: 16x^2 - 30x + 20 = 0

Step 3: Divide the equation by 2 to simplify further:

8x^2 - 15x + 10 = 0

Step 4: Attempt to factor the quadratic equation. However, it seems that this quadratic equation cannot be easily factored into linear terms with real coefficients. Therefore, we'll use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 8, b = -15, and c = 10. Plug these values into the formula:

x = (-(-15) ± √((-15)² - 4(8)(10))) / (2(8))

x = (15 ± √(225 - 320)) / 16

x = (15 ± √(-95)) / 16

Since the discriminant (the value inside the square root) is negative, there are no real solutions to this equation. The solutions will be complex numbers. Therefore, the equation has no real solutions.

So, the original equation (5x-4)^2 - (3x-2)(3x+2) = 2x(8x-5) has no real solutions.