Question

2 x² + X / 3 мінус x + 3 / 4=x-1​

Answer 1

4(2x²+х)-3(х+3)=12х-12

8x²+4х-3х-9=12х-12

8x²+х-9-12х+12=0

8x²-11+3=0

а=8; b= -11; с=3

Д=b²-4ac= (-11)²-4*8*3= 25

х1,2= -b±$\sqrt{Д}$Д / 2а

х1= 11+5 / 16= 1

х2= 11-5 / 16= 3/8

Answer 2

To solve the equation 2x² + x/3 - x + 3/4 = x - 1, follow these steps:

1. Combine like terms on both sides of the equation: 2x² + x/3 - x + 3/4 = x - 1

   First, let's simplify the left side of the equation: 2x² + (1/3)x - x + 3/4 = x - 1 2x² - (2/3)x + 3/4 = x - 1

2. Move all terms to one side of the equation to set it equal to zero: 2x² - (2/3)x + 3/4 - x + 1 = 0 2x² - (2/3)x - x + 7/4 = 0

3. Combine like terms again: 2x² - (2/3)x - (3/3)x + 7/4 = 0 2x² - (5/3)x + 7/4 = 0

4. To make the coefficients integers, multiply the entire equation by 12 (the least common multiple of 3 and 4): 12 * (2x² - (5/3)x + 7/4) = 12 * 0 24x² - 20x + 21 = 0

5. Now we have a quadratic equation: 24x² - 20x + 21 = 0. To solve for x, you can use the quadratic formula:

   x = (-b ± √(b² - 4ac)) / 2a

   In this case, a = 24, b = -20, and c = 21.

   x = (-(-20) ± √((-20)² - 4 * 24 * 21)) / (2 * 24) x = (20 ± √(400 - 2016)) / 48 x = (20 ± √(-1616)) / 48

   Since the discriminant (b² - 4ac) is negative, the solutions will involve imaginary numbers.

   x = (20 ± √(1616)i) / 48

So, the solutions are: x = (20 + √(1616)i) / 48 x = (20 - √(1616)i) / 48

These are the complex solutions to the given equation.