Question

100x²-6.25=0 разность квадратов двух выражений, уравнение. Хэлп.

Answer 1

(10х-2,5)(10х+2,5)=О
10х -2,5=0 и 10х+2,5=0
х=0,4 и х=-0,4
Ответ: -0,4; 0,4

Answer 2

Quadratic Equation and Difference of Squares

To solve the equation 100x² - 6.25 = 0, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, we can rewrite the equation as a difference of squares:

100x² - 6.25 = (10x)² - (2.5)²

Applying the Difference of Squares Formula

Using the difference of squares formula, we can express the equation as:

(10x + 2.5)(10x - 2.5) = 0

Solving for x

Now, we can solve for x by setting each factor equal to zero:

1. 10x + 2.5 = 0 2. 10x - 2.5 = 0

Solving for x in the First Equation

For the first equation, 10x + 2.5 = 0, we can solve for x as follows:

10x = -2.5

x = -2.5 / 10

x = -0.25

Solving for x in the Second Equation

For the second equation, 10x - 2.5 = 0, we can solve for x as follows:

10x = 2.5

x = 2.5 / 10

x = 0.25

Final Solutions

Therefore, the solutions to the equation 100x² - 6.25 = 0 are:

x = -0.25 and x = 0.25