Ответы
1) (x+3)² + (2x-4)(2x+4) = 5x² + 2
Expanding the equation:
x² + 6x + 9 + (2x-4)(2x+4) = 5x² + 2
Simplifying the right side:
x² + 6x + 9 + 4x² - 16 = 5x² + 2
Combining like terms:
5x² + 6x - 7 = 5x² + 2
Subtracting 5x² from both sides:
6x - 7 = 2
Adding 7 to both sides:
6x = 9
Dividing both sides by 6:
x = 9/6
Simplifying:
x = 3/2
2) (x+2)² - (x-3)² = 20
Using the difference of squares:
[(x+2) + (x-3)][(x+2) - (x-3)] = 20
Simplifying:
[2x - 1][6] = 20
Dividing both sides by 6:
2x - 1 = 20/6
Simplifying:
2x - 1 = 10/3
Adding 1 to both sides:
2x = 10/3 + 1
Simplifying:
2x = 10/3 + 3/3
2x = 13/3
Dividing both sides by 2:
x = 13/6
3) 5x² - 10x = 0
Factoring out a common factor:
5x(x - 2) = 0
Setting each factor equal to 0:
5x = 0 or x - 2 = 0
Solving for x in each equation:
x = 0 or x = 2
4) x² - 11x + 10 = 0
This equation can be factored as:
(x - 10)(x - 1) = 0
Setting each factor equal to 0:
x - 10 = 0 or x - 1 = 0
Solving for x in each equation:
x = 10 or x = 1