Question

Solve the radical equation x-2" alt="\sqrt{2-x} = x-2" align="absmiddle" class="latex-formula">

Answer 1

Answer:

x = 1 or 2

Step-by-step explanation:

$\sqrt{2 - x} = x - 2$

Squaring both the sides ,

$= > { (\sqrt{2 - x}) }^{2} = {(x - 2)}^{2}$

$= >2 - x = {x}^{2} - 4x + 4$

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) $x - 2 = 0$

$= > x = 2$