Question

(корень)17+2x-3x^2=x+1

Answer 1

√(17+2x-3x^2)=x+1

(возводим обе части ур-ия в квадрат )

17+2x-3x^2=x^2+2x+1

16-4x^2=0

4x^2=16

x^2=4

x=±2, x=-2 посторонний корень

ответ: x=2

Answer 2

To solve the equation √17 + 2x - 3x² = x + 1, we can follow these steps:

1. Rearrange the equation to have all terms on one side: -3x² + 2x + (√17 - x - 1) = 0

2. Simplify the expression within the parentheses: -3x² + 2x - x + (√17 - 1) = 0 -3x² + x + (√17 - 1) = 0

3. Apply the quadratic formula to solve for x: The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using: x = (-b ± √(b² - 4ac)) / (2a)

   In our case, a = -3, b = 1, and c = (√17 - 1).

   x = (-1 ± √(1 - 4(-3)(√17 - 1))) / (2(-3)) x = (-1 ± √(1 + 12(√17 - 1))) / (-6) x = (-1 ± √(1 + 12√17 - 12)) / (-6) x = (-1 ± √(-11 + 12√17)) / (-6)

4. Evaluate the solutions for x: The solutions will depend on the value within the square root. If -11 + 12√17 is negative, the equation has no real solutions.

   -11 + 12√17 ≈ -11 + 12(4.123) ≈ -11 + 49.476 ≈ 38.476

   Since 38.476 is positive, there are real solutions.

   x = (-1 + √(-11 + 12√17)) / (-6) x = (-1 - √(-11 + 12√17)) / (-6)

These are the solutions to the equation √17 + 2x - 3x² = x + 1.