Question

√(x-5) + √(10-x) = 3

Answer 1

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Готово!!Удачи:))

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Answer 2

Ответ:

см на рисунке

Пошаговое объяснение:

Answer 3

To solve the equation √(x-5) + √(10-x) = 3, we need to isolate x. Here's how you can do it step-by-step:

Step 1: Isolate one of the square root terms on one side of the equation. Let's isolate √(x-5):

√(x-5) = 3 - √(10-x)

Step 2: Square both sides of the equation to eliminate the square root on the left side:

(√(x-5))^2 = (3 - √(10-x))^2

Step 3: Simplify the right side:

(x - 5) = (3 - √(10-x)) * (3 - √(10-x))

Step 4: Expand the right side using the FOIL method (First, Outer, Inner, Last):

x - 5 = 9 - 3√(10-x) - 3√(10-x) + (10 - x)

Step 5: Combine like terms:

x - 5 = 9 - 2(3√(10-x)) + 10 - x

Step 6: Move all x terms to one side and constants to the other side:

x + x = 9 - 5 + 10 - 2(3√(10-x))

2x = 14 - 2(3√(10-x))

Step 7: Divide by 2:

x = 7 - 3√(10-x)

Step 8: Square both sides again to eliminate the square root:

x^2 = (7 - 3√(10-x))^2

Step 9: Expand the right side:

x^2 = 49 - 42√(10-x) + 9(10-x)

Step 10: Move all terms to one side:

x^2 - 49 + 42√(10-x) - 9(10-x) = 0

This is a quadratic equation in terms of √(10-x). Let's solve for √(10-x):

42√(10-x) = x^2 - 49 + 9(10-x)

Step 11: Isolate √(10-x) by dividing both sides by 42:

√(10-x) = (x^2 - 49 + 9(10-x)) / 42

Step 12: Square both sides again to eliminate the square root:

(√(10-x))^2 = [(x^2 - 49 + 9(10-x)) / 42]^2

10 - x = (x^2 - 49 + 9(10-x))^2 / 42^2

Step 13: Simplify the right side:

10 - x = (x^2 - 49 + 90 - 9x)^2 / 1764

10 - x = (x^2 - 9x + 41)^2 / 1764

Step 14: Move all terms to one side:

0 = (x^2 - 9x + 41)^2 / 1764 - (10 - x)

0 = (x^2 - 9x + 41)^2 / 1764 + x - 10

Step 15: Multiply both sides by 1764 to eliminate the fraction:

0 = (x^2 - 9x + 41)^2 + 1764(x - 10)

Step 16: Expand the squared term:

0 = (x^4 - 18x^3 + 122x^2 - 378x + 1681) + 1764x - 17640

Step 17: Simplify the equation:

0 = x^4 - 18x^3 + 122x^2 + 1386x - 15959

Now, we have a fourth-degree polynomial equation in terms of x. Solving this equation may not be straightforward. You can try using numerical methods or graphing techniques to find approximate solutions. Additionally, the solutions might involve complex numbers, depending on the values of x.