The answer to the question is 3
Isolate the square root from the left hand side √x-3 = 3-x
Eliminate the radical on the left hand side by squaring on both sides-
Both sides must be raised to the second power.
(√x-3)² = (3-x)²
After squaring we get
x-3 = x²-6x+9
Solving the quadratic equation-
We get rearranged equation as -
x² - 7x + 12 = 0
(x-4)(x-3)=0
x=4,3
Check if the first solution is correct by putting it in original equation-
putting x=3 in 3-√(x-3)=x we get 3-0=3
Hence 3 is correct.
Check if the second solution is correct by putting it in original equation-
putting x=4 in 3-√(x-3)=x we get 3-1=4 which is not true
hence 4 is rejected.
Therefore, the ultimate answer to the question is x=3.
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