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LuckyWell [14K]
3 years ago
13

Solve the radical equation

x-2" alt="\sqrt{2-x} = x-2" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Gemiola [76]3 years ago
3 0

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

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