Question

Найдите корень уравнения...

Answer 1

Обе части неотрицательные, значит можно возводить в квадрат, но сначала нужно найти ОДЗ:
при решении пригодится свойство пропорции:произведение средних членов равно произведению крайних членов (а/b=с/d ⇔ad=bc)

Answer 2

Finding the Root of an Equation

To find the root of an equation, we need to solve for the value of the variable that satisfies the equation. Here are some examples of equations and their roots:

1. Equation: 6 - 5 = 7 - Root: There is no solution to this equation. The left side of the equation simplifies to 1, which is not equal to 7.

2. Equation: 4x - 7 = 2x - Root: To find the root, we need to isolate the variable x. Subtracting 2x from both sides of the equation gives us 2x - 7 = 0. Adding 7 to both sides gives us 2x = 7. Finally, dividing both sides by 2 gives us x = 7/2 = 3.5.

3. Equation: x + 1/8 = 1/2 - Root: To find the root, we need to isolate the variable x. Subtracting 1/8 from both sides of the equation gives us x = 1/2 - 1/8. Simplifying the right side gives us x = 4/8 - 1/8 = 3/8.

4. Equation: x^2 - 3x - 18 = 0 - Root: To find the root, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots are given by the formula x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 1, b = -3, and c = -18. Plugging these values into the formula, we get x = (3 ± √(9 + 72)) / 2. Simplifying further, we have x = (3 ± √81) / 2. The square root of 81 is 9, so the roots are x = (3 ± 9) / 2. Therefore, the roots of the equation are x = 6 and x = -3.

5. Equation: 1/2 + x = 3/4 - Root: To find the root, we need to isolate the variable x. Subtracting 1/2 from both sides of the equation gives us x = 3/4 - 1/2. Simplifying the right side gives us x = 6/8 - 4/8 = 2/8 = 1/4.

6. Equation: 14/(x - 3) = -(7/9) - Root: To find the root, we need to isolate the variable x. Multiplying both sides of the equation by (x - 3) gives us 14 = -(7/9)(x - 3). Simplifying the right side gives us 14 = -(7/9)x + 7/3. Subtracting 7/3 from both sides gives us 14 - 7/3 = -(7/9)x. Simplifying further, we have 42/3 - 7/3 = -(7/9)x. Combining like terms gives us 35/3 = -(7/9)x. Multiplying both sides by 9/7 gives us (35/3)(9/7) = x. Simplifying further, we have x = 105/21 = 5.

7. Equation: -2x - 7 = -4x - Root: To find the root, we need to isolate the variable x. Adding 4x to both sides of the equation gives us 2x - 7 = 0. Adding 7 to both sides gives us 2x = 7. Finally, dividing both sides by 2 gives us x = 7/2 = 3.5.

8. Equation: (x - 3)(x - 7) - (x - 9)(x + 9) = 24 - Root: To find the root, we need to expand and simplify the equation. Expanding the equation gives us x^2 - 3x - 7x + 21 - (x^2 - 9x + 9x - 81) = 24. Simplifying further, we have x^2 - 10x + 21 - x^2 + 9x - 9x + 81 = 24. Combining like terms gives us -10x + 21 + 81 = 24. Simplifying further, we have -10x + 102 = 24. Subtracting 102 from both sides gives us -10x = -78. Finally, dividing both sides by -10 gives us x = -78/-10 = 39/5.

9. Equation: (x - 105)/(x + 3) = -5 - Root: To find the root, we need to isolate the variable x. Multiplying both sides of the equation by (x + 3) gives us x - 105 = -5(x + 3). Expanding the right side gives us x - 105 = -5x - 15. Adding 5x to both sides gives us 6x - 105 = -15. Adding 105 to both sides gives us 6x = 90. Finally, dividing both sides by 6 gives us x = 90/6 = 15.

Please let me know if you have any further questions!