Question

Решите 4х^2/(1-х)*(1-х) =50

Answer 1

$\frac{4 {x}^{2} }{{(1 - x)}^{2} } = 50$
х≠1

$( \frac{2x}{(1 - x) } ) ^{2} = 50$
откуда имеем 2 уравнения
$\frac{2x}{(1 - x) } = 5 \sqrt{2} \: и \: \\ \frac{2x}{(1 - x) } = - 5 \sqrt{2}$

решаем первое уравнение
2х=5√2-x•5✓2
откуда (2+5√2)•х=5√2
или х1=5√2/(2+5√2)

решаем второе
2х=-5√2+x•5✓2
(5✓2-2)•х=5√2
х2=5✓2/(5✓2-2)

оба решения удовлетворяют ОДЗ х≠1
и подходят нам

Ответ
х1=5√2/(2+5√2)
х2=5✓2/(5✓2-2)

Answer 2

Решение во вложении. Удачи

Answer 3

To solve the equation, we first need to simplify it:

4x^2 / ((1 - x) * (1 - x)) = 50

Now, let's get rid of the denominator on the left side of the equation by multiplying both sides by ((1 - x) * (1 - x)):

4x^2 = 50 * ((1 - x) * (1 - x))

Next, expand the right side of the equation:

4x^2 = 50 * (1 - 2x + x^2)

Now distribute 50:

4x^2 = 50 - 100x + 50x^2

Bring everything to one side of the equation to form a quadratic equation:

4x^2 - 50x^2 + 100x - 50 = 0

Combine like terms:

-46x^2 + 100x - 50 = 0

Now, let's solve this quadratic equation for x. We can do this by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation:

a = -46, b = 100, c = -50

x = (-(100) ± √((100)^2 - 4*(-46)(-50))) / 2(-46) x = (-100 ± √(10000 - 9200)) / (-92) x = (-100 ± √800) / (-92) x = (-100 ± 20√2) / (-92)

Now, we have two solutions for x:

1. x = (-100 + 20√2) / (-92)
2. x = (-100 - 20√2) / (-92)

These are the exact solutions for the equation. If you want decimal approximations, you can calculate them using a calculator.