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If x is the solution to the equation
√(x-3) = 3-√(x), what is the value of
√(x-3)?

A. 1
B.
\sqrt{(3)/(2)}
C.
√(3)
D. 3

1 Answer

5 votes

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.

User Aezell
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