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

Question

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

Answer 1

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`