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Answer:
x = 1 or 2
Step-by-step explanation:
[tex] \sqrt{2 - x} = x - 2[/tex]
Squaring both the sides ,
[tex] = > { (\sqrt{2 - x}) }^{2} = {(x - 2)}^{2} [/tex]
[tex] = >2 - x = {x}^{2} - 4x + 4[/tex]
Adding like terms ,
[tex] = > {x}^{2} - 4x + x + 4 - 2 = 0[/tex]
[tex] = > {x}^{2} - 3x + 2 = 0[/tex]
Factorising the eqn. ,
[tex] = > {x}^{2} - x - 2x + 2 = 0[/tex]
[tex] = > x(x - 1) - 2(x - 1) = 0[/tex]
[tex] = > (x - 1)(x - 2) = 0[/tex]
Here x will have 2 values .
1) [tex]x - 1 = 0[/tex]
[tex] = > x = 1[/tex]
2) [tex]x - 2 = 0[/tex]
[tex] = > x = 2[/tex]