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Solve the radical equation [tex]\sqrt{2-x} = x-2[/tex]

Sagot :

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]