Question

media geometrica si aritmetica a numerelor a si b.
$a = 2 \sqrt{5} - 3 \sqrt{2}$
$b = 3 \sqrt{2} + 2 \sqrt{5}$
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Answer 1

→ mg= √(a×b)

a= 2√5 -3√2

b= 3√2 +2√5

→

$m _{g} = \sqrt{(2 \sqrt{5} - 3 \sqrt{2})(3 \sqrt{2} + 2 \sqrt{5}) } \\ m_{g} = \sqrt{(2 \sqrt{5} - 3 \sqrt{2})(2 \sqrt{5} + 3 \sqrt{2} ) } \\ m _{g} = \sqrt{(2 \sqrt{5}) {}^{2} - (3 \sqrt{2} ) {}^{2} } \\ m _{g} = \sqrt{20 - 18} \\ m _{g} = \sqrt{2}$

→ ma= (a+b)/2

→ ma= (2√5 -3√2+ 3√2 +2√5)/2 => ma= 4√5/2 => ma= 2√5