Question

2) (1,2 - x)(x + 1,2) +1,8x + x2 = 0; 3) 0,49x2 - 3x - (0,7x + 2)(0,7 x - 2) = 0;4) (1,6x + 1)(1 - 1,6x) - 64x(1 - 0,04x) = 0.​

Answer 1

Ответ:

Объяснение:

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Answer 2

To solve each of these quadratic equations, we can follow the standard procedure of expanding and simplifying the expressions, then setting them equal to zero, and finally using the quadratic formula to find the solutions. Let's solve each equation step by step:

1. (1.2 - x)(x + 1.2) + 1.8x + x^2 = 0

Expand the equation: (x - 1.2)(x + 1.2) + 1.8x + x^2 = 0 (x^2 + 1.2x - 1.2x - 1.44) + 1.8x + x^2 = 0 x^2 + x^2 + 1.8x - 1.44 = 0 2x^2 + 1.8x - 1.44 = 0

Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = 1.8, and c = -1.44.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions:

x = [-(1.8) ± √((1.8)^2 - 4 * 2 * (-1.44))] / 2 * 2 x = [-1.8 ± √(3.24 + 11.52)] / 4 x = [-1.8 ± √14.76] / 4

x = (-1.8 + √14.76) / 4 ≈ 0.484 x = (-1.8 - √14.76) / 4 ≈ -0.934

So, the solutions are approximately x = 0.484 and x = -0.934.

2. 0.49x^2 - 3x - (0.7x + 2)(0.7x - 2) = 0

Expand the equation: 0.49x^2 - 3x - (0.49x^2 - 2.8x + 4) = 0 0.49x^2 - 3x - 0.49x^2 + 2.8x - 4 = 0 -0.21x + 2.8 - 4 = 0 -0.21x - 1.2 = 0

Now, we have a linear equation in the form ax + b = 0, where a = -0.21, and b = -1.2.

Solving for x: -0.21x = 1.2 x = 1.2 / -0.21 x ≈ -5.714

So, the solution is approximately x = -5.714.

3. (1.6x + 1)(1 - 1.6x) - 64x(1 - 0.04x) = 0

Expand the equation: (1.6x + 1 - 1.6x + 2.56x^2) - (64x - 2.56x^2) = 0 1 + 2.56x^2 - 64x + 2.56x^2 = 0 5.12x^2 - 64x + 1 = 0

Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 5.12, b = -64, and c = 1.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions:

x = [-(64) ± √((-64)^2 - 4 * 5.12 * 1)] / 2 * 5.12 x = [-64 ± √(4096 - 20.48)] / 10.24 x = [-64 ± √4075.52] / 10.24

x = (-64 + √4075.52) / 10.24 ≈ 6.211 x = (-64 - √4075.52) / 10.24 ≈ -6.211

So, the solutions are approximately x = 6.211 and x = -6.211.

Note: For all these equations, there might be some rounding errors in the final solutions due to the approximations made during the calculations.