Question

aratati ca numarul x este numar natural, unde: d)
$\sqrt{21 - 12 \sqrt{3} } - \sqrt{30 + 12 \sqrt{6} } + 3 \sqrt{6 + 4 \sqrt{2} }$
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Answer 1

√(21-12√3) - √(30+12√6) + 3√(6+4√2) =

= √(3-2√3)² - √(2√3+3√2)² + 3√(√2+2)² = (2√3-2) - (2√3+3√2) + 3(√2+2) =

= 2√3 - 2√3 - 2 + 6 - 3√2 + 3√2 = 4 ∈ N