Question

7 класс (7x-6)²-81=0 (6c-4)²-(4c+3)²=0 (x-3)²+(x+2)²=2(3-x)(x+2)

Answer 1

Как-то так. Пожалуйста

Answer 2

To solve the equations, let's take them one by one:

1. (7x - 6)² - 81 = 0

Step 1: Expand the squared term: (7x - 6)² = (7x - 6)(7x - 6) = 49x² - 84x + 36

Step 2: Rewrite the equation with the expanded squared term: 49x² - 84x + 36 - 81 = 0

Step 3: Combine like terms: 49x² - 84x - 45 = 0

Step 4: Factor the quadratic equation: (7x - 9)(7x + 5) = 0

Step 5: Solve for x: 7x - 9 = 0 --> 7x = 9 --> x = 9/7 7x + 5 = 0 --> 7x = -5 --> x = -5/7

So the solutions for this equation are x = 9/7 and x = -5/7.

2. (6c - 4)² - (4c + 3)² = 0

Step 1: Expand the squared terms: (6c - 4)² = (6c - 4)(6c - 4) = 36c² - 48c + 16 (4c + 3)² = (4c + 3)(4c + 3) = 16c² + 24c + 9

Step 2: Rewrite the equation with the expanded squared terms: 36c² - 48c + 16 - (16c² + 24c + 9) = 0

Step 3: Combine like terms: 36c² - 48c + 16 - 16c² - 24c - 9 = 0

Step 4: Simplify the equation: 20c² - 72c + 7 = 0

Unfortunately, this equation doesn't factor easily, so we'll have to use the quadratic formula to find the solutions for c:

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

For our equation, a = 20, b = -72, and c = 7.

Step 5: Substitute the values into the quadratic formula: c = (72 ± √((-72)² - 4 * 20 * 7)) / 2 * 20

Step 6: Calculate the discriminant: Discriminant = (-72)² - 4 * 20 * 7 = 5184 - 560 = 4624

Step 7: Continue solving for c: c = (72 ± √4624) / 40 c = (72 ± 68) / 40

So the two solutions for c are: c = (72 + 68) / 40 = 140 / 40 = 3.5 c = (72 - 68) / 40 = 4 / 40 = 0.1

Thus, the solutions for this equation are c = 3.5 and c = 0.1.

3. (x - 3)² + (x + 2)² = 2(3 - x)(x + 2)

Step 1: Expand the squared terms: (x - 3)² = (x - 3)(x - 3) = x² - 6x + 9 (x + 2)² = (x + 2)(x + 2) = x² + 4x + 4

Step 2: Rewrite the equation with the expanded squared terms: x² - 6x + 9 + x² + 4x + 4 = 2(3 - x)(x + 2)

Step 3: Combine like terms: 2x² - 2x + 13 = 2(3 - x)(x + 2)

Step 4: Distribute on the right side: 2x² - 2x + 13 = 2(3x + 6 - x² - 2x)

Step 5: Simplify the right side: 2x² - 2x + 13 = 2(6 - x²)

Step 6: Expand the right side: 2x² - 2x + 13 = 12 - 2x²

Step 7: Move all terms to one side of the equation: 2x² - 2x + 13 - 12 + 2x² = 0

Step 8: Combine like terms: 4x² - 1 = 0

Step 9: Factor the quadratic equation: (2x - 1)(2x + 1) = 0

Step 10: Solve for x: 2x - 1 = 0 --> 2x = 1 --> x = 1/2 2x + 1 = 0 --> 2x = -1 --> x = -1/2

So the solutions for this equation are x = 1/2 and x = -1/2.