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Solve the radical equation
√(2-x) = x-2

1 Answer

7 votes

Answer:

x = 1 or 2

Explanation:


√(2 - x) = x - 2

Squaring both the sides ,


= > { (√(2 - x)) }^(2) = {(x - 2)}^(2)


= >2 - x = {x}^(2) - 4x + 4

Adding like terms ,


= > {x}^(2) - 4x + x + 4 - 2 = 0


= > {x}^(2) - 3x + 2 = 0

Factorising the eqn. ,


= > {x}^(2) - x - 2x + 2 = 0


= > x(x - 1) - 2(x - 1) = 0


= > (x - 1)(x - 2) = 0

Here x will have 2 values .

1)
x - 1 = 0


= > x = 1

2)
x - 2 = 0


= > x = 2

User Steven Johnston
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