Compute the numeric value of 4 + 7 − 4 − 7 . Express the answer in simplest radical form.
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x = 4 + 7 − 4 − 7 = ( 2 7 + 1 ) 2 − ( 2 7 − 1 ) 2 = 2 7 + 1 − 2 7 − 1 = 2 2 = 2
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( 4 + 7 − 4 − 7 ) 2
= ( 4 + 7 ) + ( 4 − 7 ) − 2 ( 4 + 7 ) ( 4 − 7 )
= 8 − 2 9
= 2
So, 4 + 7 − 4 − 7 = 2