Question

5p 5. Media geometrică a numerelor a = 2√3-3 şi b=3+2√3 este:​

Answer 1

Răspuns:

Explicație pas cu pas:

mg=√ab

mg=√(2√3-3)√(2√3+3)=√(12-9)=√3

am folosit formula (x+y)(x-y)=x²-y²

Answer 2

$\displaystyle a=2\sqrt{3} -3;~b=3+2\sqrt{3}\\\\ m_g=\sqrt{a \cdot b}=\sqrt{\Big(2\sqrt{3} -3\Big)\Big(3+2\sqrt{3} \Big)} =\sqrt{\Big(2\sqrt{3} \Big)^2-3^2} =\\\\ =\sqrt{2^2 \cdot \Big(\sqrt{3}\Big)^2 -9} =\sqrt{4 \cdot 3-9}=\sqrt{12-9}=\sqrt{3} \\\\\boxed{m_g=\sqrt{3} }$