Question

(12у+18)•(1,6-0,2у)=0

Answer 1

1 способ.

Чтобы произведение равнялось 0, достаточно, чтобы один из множителей был равен 0.

(12у + 18) · (1,6 - 0,2у) = 0

12у + 18 = 0             или            1,6 - 0,2у = 0

12у = -18                                     0,2у = 1,6

у = -18 : 12                                  у = 1,6 : 0.2

у = -1,5                                        у = 8

2 способ.

(12у + 18) · (1,6 - 0,2у) = 0

19,2у + 28,8 - 2,4у² - 3,6у = 0

-2,4у² + 15,6у + 28,8 = 0

D = b² - 4ac = (15,6)² - 4 · (-2,4) · 28,8 = 243,36 + 276,48 = 519,84

√D = √519,84 = 22,8

у₁ = (-15,6-22,8)/(2·(-2,4)) = (-38,4)/(-4,8) = 8

у₂ = (-15,6+22,8)/(2·(-2,4)) = (7,2)/(-4,8) = -1,5

Ответ: (-1,5; 8).

Answer 2

To solve the equation (12у + 18) * (1.6 - 0.2у) = 0, we need to find the values of 'у' that satisfy the equation.

Let's break down the equation and solve it step by step:

(12у + 18) * (1.6 - 0.2у) = 0

Distribute the terms in the parentheses: 12у * 1.6 - 12у * 0.2у + 18 * 1.6 - 18 * 0.2у = 0

Simplify the terms: 19.2у - 2.4у^2 + 28.8 - 3.6у = 0

Combine like terms: 19.2у - 3.6у - 2.4у^2 + 28.8 = 0

Combine the numerical terms: 15.6у - 2.4у^2 + 28.8 = 0

Now we have a quadratic equation in terms of 'у'. To solve for 'у', we can use the quadratic formula:

у = (-b ± √(b^2 - 4ac)) / 2a

In this equation, 'a' is the coefficient of у^2, 'b' is the coefficient of у, and 'c' is the constant term.

For our equation, a = -2.4, b = 15.6, and c = 28.8. Plugging these values into the quadratic formula:

у = (-(15.6) ± √((15.6)^2 - 4 * (-2.4) * 28.8)) / (2 * -2.4)

Calculating the discriminant: Discriminant = (15.6)^2 - 4 * (-2.4) * 28.8 = 243.36 + 275.52 = 518.88

Plugging the discriminant back into the formula: у = (-15.6 ± √518.88) / -4.8

Calculating the square root of the discriminant: √518.88 ≈ 22.799

Now we have two possible solutions for 'у':

1. у = (-15.6 + 22.799) / -2.4 ≈ 2.667
2. у = (-15.6 - 22.799) / -2.4 ≈ -16.667

So, the solutions for the equation are approximately у ≈ 2.667 and у ≈ -16.667. These values make the original equation (12у + 18) * (1.6 - 0.2у) equal to 0.