Sqrt(x-2)+sqrt(5)=sqrt(20)

Предыдущий
вопрос Следующий
вопрос

To solve this equation, we need to isolate the variable x.

First, we will square both sides of the equation to get rid of the square roots:

(Sqrt(x-2) + Sqrt(5))^2 = Sqrt(20)^2
(x-2) + 2Sqrt(x-2)*Sqrt(5) + 5 = 20

Now we can simplify the equation by expanding the left side:

x - 2 + 2Sqrt(5(x-2)) + 5 = 20
x + 3 + 2Sqrt(5x - 10) = 20

Next, we can isolate the square root term on one side of the equation and move the other terms to the other side:

2Sqrt(5x - 10) = 20 - x - 3
2Sqrt(5x - 10) = 17 - x

Now, square both sides to eliminate the square root term:

(2Sqrt(5x - 10))^2 = (17 - x)^2
4(5x - 10) = (17 - x)(17 - x)
20x - 40 = 289 - 34x + x^2
x^2 + 54x - 329 = 0

Now we have a quadratic equation that we can solve using the quadratic formula:

x = (-54 ± sqrt(54^2 - 4(1)(-329))) / 2(1)
x = (-54 ± sqrt(2916 + 1316)) / 2
x = (-54 ± sqrt(4232)) / 2
x = (-54 ± 65.071) / 2

Now we have two possible solutions for x:

x1 = (-54 + 65.071) / 2 = 11.071
x2 = (-54 - 65.071) / 2 = -59.071

Therefore, the solutions to the equation are x = 11.071 and x = -59.071.