Question

Найдите корень уровнения

Answer 1

$\dfrac{9x-3}{x+5}=0\qquad(x\not=-5)\\ 9x-3=0\\ 9x=3\\ x=\dfrac{3}{9}=\dfrac{1}{3}$

Answer 2

Solving the Equation

To find the root of the equation, we can refer to the search results. Let's examine the available sources:

- Source provides an equation: x + 5x - 14 = 0. - Source provides an equation: 4x - 7 = 2x. - Source provides an equation: 4x - 7 = 2x. - Source provides an equation: x^2 - 3x - 18 = 0. - Source provides an equation: (x - 3)(x - 7) - (x - 9)(x + 9) = 24.

Let's solve each equation one by one:

1. Equation: x + 5x - 14 = 0. - Combining like terms, we get: 6x - 14 = 0. - Adding 14 to both sides, we have: 6x = 14. - Dividing both sides by 6, we find: x = 14/6. - Simplifying the fraction, we get: x = 7/3.

2. Equation: 4x - 7 = 2x. - Subtracting 2x from both sides, we get: 2x - 7 = 0. - Adding 7 to both sides, we have: 2x = 7. - Dividing both sides by 2, we find: x = 7/2. - Simplifying the fraction, we get: x = 3.5.

3. Equation: 4x - 7 = 2x. - Subtracting 2x from both sides, we get: 2x - 7 = 0. - Adding 7 to both sides, we have: 2x = 7. - Dividing both sides by 2, we find: x = 7/2. - Simplifying the fraction, we get: x = 3.5.

4. Equation: x^2 - 3x - 18 = 0. - This equation is a quadratic equation. - We can solve it using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). - Plugging in the values, we have: x = (-(-3) ± √((-3)^2 - 4(1)(-18))) / (2(1)). - Simplifying, we get: x = (3 ± √(9 + 72)) / 2. - Further simplifying, we have: x = (3 ± √81) / 2. - Taking the square root, we get: x = (3 ± 9) / 2. - This gives us two solutions: x = (3 + 9) / 2 and x = (3 - 9) / 2. - Simplifying, we find: x = 6 and x = -3.

5. Equation: (x - 3)(x - 7) - (x - 9)(x + 9) = 24. - Expanding the equation, we get: x^2 - 3x - 7x + 21 - (x^2 - 9x + 9x - 81) = 24. - Simplifying, we have: x^2 - 10x + 21 - x^2 + 81 = 24. - Combining like terms, we get: -10x + 102 = 24. - Subtracting 102 from both sides, we have: -10x = -78. - Dividing both sides by -10, we find: x = 78/10. - Simplifying the fraction, we get: x = 39/5.

To summarize, the roots of the given equations are as follows:

- Equation 1: x = 7/3 - Equation 2: x = 3.5 - Equation 3: x = 3.5 - Equation 4: x = 6 and x = -3 - Equation 5: x = 39/5

Please let me know if there's anything else I can help you with!