Final answer:
To find the value of √(x-3), solve the equation √(x-3) = 3 - √x. Isolate the square roots, square both sides, and simplify to obtain a quadratic equation. Solve the quadratic equation to find that x = 1 and x = 9. Since √(x-3) is only defined for x ≥ 3, the value of √(x-3) is 1.
Step-by-step explanation:
To find the value of √(x-3), we need to solve the equation √(x-3) = 3 - √x.
We can start by isolating the square root terms on one side of the equation:
√(x-3) + √x = 3
Next, we need to square both sides of the equation to eliminate the square roots:
(√(x-3) + √x)2 = 32
Expanding the left side gives:
(x-3) + 2√x√(x-3) + x = 9
Combining like terms:
2x - 3 + 2√x√(x-3) = 9
Now, we can isolate the square root term:
2√x√(x-3) = 12 - 2x
Dividing both sides by 2 gives:
√x√(x-3) = 6 - x/2
Squaring both sides again:
x(x-3) = (6 - x/2)2
Expanding the right side and rearranging the equation gives a quadratic:
x2 - 7x + 9 = 0
We can solve this quadratic equation using factoring or the quadratic formula. The solutions are x = 1 and x = 9. Since the square root of a negative number is undefined, √(x-3) is only defined for x ≥ 3. Therefore, the value of √(x-3) is 1.