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Mathematics

Grade-11

Easy

Question

Use the zero-product property to solve
$2 minus x squared equals left parenthesis 2 minus x right parenthesis squared$ .

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The correct answer is: 1

$2 minus x squared equals left parenthesis 2 minus x right parenthesis squared 2 minus x squared equals left parenthesis 2 minus x right parenthesis left parenthesis 2 minus x right parenthesis 2 minus x squared equals 4 minus 4 x plus x squared 2 minus x squared minus 2 plus x squared equals 4 minus 4 x plus x squared minus 2 plus x squared 0 equals 2 x squared minus 4 x plus 2 1 half times 0 equals 1 half times open parentheses 2 x squared minus 4 x plus 2 close parentheses 0 equals x squared minus 2 x plus 1 0 equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 1 right parenthesis x minus 1 equals 0 x minus 1 plus 1 equals 0 plus 1 x equals 1$
The solution is 1. The solution set is {1}.

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