Question

1) -x²-3x+2=0 2) x²-2x-5/(x-3)(x-1)+ 1/x-3=1 3) 1- x-3/2=x- 3(5-2x)/7

Answer 1

Відповідь:

Покрокове пояснення:

Answer 2

To solve these equations, let's go through them one by one:

1. -x² - 3x + 2 = 0

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

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / 2a

For the equation -x² - 3x + 2 = 0, the coefficients are: a = -1 b = -3 c = 2

Now, plug these values into the quadratic formula:

x = (3 ± √((-3)² - 4*(-1)2)) / 2(-1) x = (3 ± √(9 + 8)) / -2 x = (3 ± √17) / -2

So, the two solutions for this equation are: x = (3 + √17) / -2 and x = (3 - √17) / -2

2. x² - 2x - 5 / (x - 3)(x - 1) + 1 / x - 3 = 1

First, let's simplify the left-hand side of the equation:

x² - 2x - 5 / (x - 3)(x - 1) + 1 / x - 3 = 1

To combine the fractions, find a common denominator, which is (x - 3)(x - 1):

(x² - 2x - 5 + (x - 1)) / (x - 3)(x - 1) = 1

Now, combine like terms:

(x² - 2x - 5 + x - 1) / (x - 3)(x - 1) = 1

(x² - x - 6) / (x - 3)(x - 1) = 1

Next, multiply both sides by (x - 3)(x - 1) to get rid of the denominator:

x² - x - 6 = (x - 3)(x - 1)

Expand the right-hand side:

x² - x - 6 = x² - 4x + 3

Now, move all terms to one side of the equation:

x² - x - 6 - x² + 4x - 3 = 0

Simplify further:

3x - 9 = 0

Now, solve for x:

3x = 9

x = 9 / 3

x = 3

3. 1 - x - 3 / 2 = x - 3(5 - 2x) / 7

First, let's simplify the left-hand side of the equation:

1 - x - 3 / 2 = x - 3(5 - 2x) / 7

To combine the fractions, find a common denominator, which is 2 * 7 = 14:

14 * (1 - x) - 7(3) = 2(x - 3(5 - 2x))

14 - 14x - 21 = 2(x - 15 + 2x)

Now, distribute the 2 on the right side:

14 - 14x - 21 = 2x - 30 + 4x

Combine like terms:

-14x - 7 = 6x - 30

Now, move all terms involving x to one side of the equation:

-14x - 6x = -30 + 7

-20x = -23

Now, solve for x:

x = (-23) / (-20)

x = 23 / 20

x ≈ 1.15

Please double-check the solutions and the steps to ensure accuracy as manual calculation may lead to errors.