Question

1) 1/2x^2 +2x+3/2=02) 9x^2 +(9-корень из 2)*x-корень из 2=0

Answer 1

1. Ответ: x = -3; -1
2. Ответ: x = -1; -корень из 2:89; корень из 2:81

1. Объяснение: если домножить все это на 2, получится x^2+4x+3=0; D = 4; x = -4±2/2= -1;-3
2. Объяснение: надо раскрыть скобки, тогда получится 9x^2+9x-корень из 2*x-корень из 2=0

Дальше надо вынести общий множитель из первых двух членов и последних двух: 9x(x+1)-корень из 2(x+1)=0;

(x+1)(9x-корень из 2) = 0

x+1 = 0 или 9x-корень из 2 = 0

x = -1             9x = корень из 2 |^2

                     81x^2 = 2

                     x^2 = 2/81

                    x = ± корень из 2/81 или ± 1/3 на корень из 2/9

Answer 2

Let's solve each equation step by step:

1. 1/2x^2 + 2x + 3/2 = 0

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

For an equation of the form ax^2 + bx + c = 0, the quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 1/2, b = 2, and c = 3/2.

Plugging these values into the formula:

x = (-(2) ± √((2)^2 - 4 * (1/2) * (3/2))) / 2 * (1/2) x = (-2 ± √(4 - 3)) / 1 x = (-2 ± √1) / 1

Now, we have two possible solutions:

1. x = (-2 + 1) = -1
2. x = (-2 - 1) = -3

So, the solutions to the equation are x = -1 and x = -3.

2. 9x^2 + (9 - √2)x - √2 = 0

This is another quadratic equation. We'll use the quadratic formula again:

In our equation, a = 9, b = (9 - √2), and c = -√2.

Plugging these values into the formula:

x = (-(9 - √2) ± √((9 - √2)^2 - 4 * 9 * (-√2))) / 2 * 9 x = (-(9 - √2) ± √(81 - 18√2 + 2 - 72√2)) / 18 x = (-(9 - √2) ± √(83 - 90√2)) / 18

Now, we have two possible solutions:

1. x = (-(9 - √2) + √(83 - 90√2)) / 18
2. x = (-(9 - √2) - √(83 - 90√2)) / 18

These solutions are a bit complex due to the presence of the square root term. You can simplify them further if necessary, but this is the general form of the solutions to the equation.