the extraneous solution for the equation √ x - 3 = x - 5 is x = 4 or x = 7.
We are given an equation:
√ x - 3 = x - 5
Raise both sides to the power 2, we get that:
x - 3 = ( x - 5 )²
x - 3 = x² + 25 - 10 x
x² - 10 x - x + 25 + 3 = 0
x² - 11 x + 28 = 0
x² - 7 x - 4 x + 28 = 0
x( x - 7) - 4( x - 7) = 0
( x - 4 ) ( x - 7 ) = 0
x = 4 or x = 7.
Therefore, we get that, the extraneous solution for the equation √ x - 3 = x - 5 is x = 4 or x = 7.
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