ЯсноПонятно24

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

First, let's simplify the equation:

3√(10 - x) - 3√(3 - x) = 1

Now, let's square both sides of the equation to eliminate the square root:

(3√(10 - x) - 3√(3 - x))^2 = 1^2 (3√(10 - x))^2 - 2(3√(10 - x))(3√(3 - x)) + (3√(3 - x))^2 = 1 9(10 - x) - 18√((10 - x)(3 - x)) + 9(3 - x) = 1 90 - 9x - 18√(30 - 13x + x^2) + 27 - 9x = 1 117 - 18x - 18√(30 - 13x + x^2) = 1 18√(30 - 13x + x^2) = 116 - 18x √(30 - 13x + x^2) = (116 - 18x) / 18 √(30 - 13x + x^2) = (58 - 9x) / 9

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

30 - 13x + x^2 = (58 - 9x)^2 / 81 30 - 13x + x^2 = (3364 - 1044x + 81x^2) / 81 30 - 13x + x^2 = 3364/81 - 1044x/81 + 81x^2/81 30 - 13x + x^2 = 41 - 13x + x^2

Now, we see that the equation simplifies to 30 = 41, which is not true. Therefore, there is no solution to the original equation 3√(10 - x) - 3√(3 - x) = 1.