Question

Calculați media geometrică a numerelor
a=|2 radical 3 minus 3 radical 2|
b=radical 48 +radical 72.

Answer 1

$a = |2 \ \sqrt{3} - 3 \sqrt{2} | = 3 \sqrt{2} - 2 \sqrt{3} \\ b = \sqrt{48} + \sqrt{72} = 4 \sqrt{3} + 6 \sqrt{2 } \\ \sqrt{ab } = \sqrt{(3 \sqrt{2} - 2 \sqrt{3})(4 \sqrt{3} + 6 \sqrt{2} ) } \\ \sqrt{ab} = \sqrt{12 \sqrt{6} + 36 - 24 - 12 \sqrt{6} } \\ \sqrt{ab} = \sqrt{12} = 2 \sqrt{3}$