[tex]( \sqrt{7 - 2 \sqrt{6} } - \sqrt{7 + 2 \sqrt{6} } ) {}^{2} = ( \sqrt{(1 - \sqrt{6} {)}^{2} } - \sqrt{(1 + \sqrt{6} ) {}^{2} } ) {}^{2} = ( \sqrt{6} - 1 - (1 + \sqrt{6} )) {}^{2} = ( \sqrt{6} - 1- 1 - \sqrt{6} ) {}^{2} = ( - 2) {}^{2} = 4[/tex]
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[tex]( \sqrt{7 - 2 \sqrt{6} } - \sqrt{7 + 2 \sqrt{6} } ) {}^{2} = ( \sqrt{(1 - \sqrt{6} {)}^{2} } - \sqrt{(1 + \sqrt{6} ) {}^{2} } ) {}^{2} = ( \sqrt{6} - 1 - (1 + \sqrt{6} )) {}^{2} = ( \sqrt{6} - 1- 1 - \sqrt{6} ) {}^{2} = ( - 2) {}^{2} = 4[/tex]