Question

Б)0,3x^2=7,5x г)1/4x^2-25=0 помогите пожалуйста

Answer 1

aх² + bх + с = 0 - общий вид квадратного уравнения

б) 0,3х² - 7,5х = 0

Разделим обе части уравнения на 0,3

х² - 25х = 0

D = b² - 4ac = (-25)² - 4 · 1 · 0 = 625 - 0 = 625

√D = √625 = 25

х = (-b±√D)/2а

х₁ = (25-25)/(2·1) = 0/2 = 0

х₂ = (25+25)/(2·1) = 50/2 = 25

Ответ: (0; 25).

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а² - b² = (a + b)(a - b) - разность квадратов

г) 1/4х² - 25 = 0

0,25х² - 5² = 0

(0,5х)² - 5² = 0

(0,5х + 5)(0,5х - 5) = 0

0,5х + 5 = 0            и             0,5х - 5 = 0

0,5х = -5                                0,5х = 5

х = -5 : 0,5                              х = 5 : 0,5

х₁ = -10                                    х₂ = 10

Ответ: (-10; 10).

Answer 2

Solving the equation 0.3x^2 = 7.5x

To solve the equation 0.3x^2 = 7.5x, we can start by rearranging the equation to bring all the terms to one side.

0.3x^2 - 7.5x = 0

Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 0.3, b = -7.5, and c = 0.

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get:

x = (-(-7.5) ± √((-7.5)^2 - 4(0.3)(0))) / (2(0.3))

Simplifying further:

x = (7.5 ± √(56.25)) / 0.6

x = (7.5 ± 7.5) / 0.6

This gives us two possible solutions:

x = (7.5 + 7.5) / 0.6 = 25

x = (7.5 - 7.5) / 0.6 = 0

Therefore, the solutions to the equation 0.3x^2 = 7.5x are x = 25 and x = 0.

Solving the equation 1/4x^2 - 25 = 0

To solve the equation 1/4x^2 - 25 = 0, we can start by isolating the x^2 term.

1/4x^2 = 25

Multiplying both sides of the equation by 4 to eliminate the fraction:

x^2 = 100

To find the solutions for x, we can take the square root of both sides:

x = ±√100

x = ±10

Therefore, the solutions to the equation 1/4x^2 - 25 = 0 are x = 10 and x = -10.

I hope this helps! Let me know if you have any further questions.