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

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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)^
(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 = 2
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 -
2Sqrt(5x - 10) = 17 - x

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

(2Sqrt(5x - 10))^2 = (17 - x)^
4(5x - 10) = (17 - x)(17 - x
20x - 40 = 289 - 34x + x^
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)) /
x = (-54 ± sqrt(4232)) /
x = (-54 ± 65.071) / 2

Now we have two possible solutions for x:

x1 = (-54 + 65.071) / 2 = 11.07
x2 = (-54 - 65.071) / 2 = -59.071

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