Explicație pas cu pas:
[tex]y = \sqrt{21 - 12 \sqrt{3} } = \sqrt{9 + 12 - 12 \sqrt{3} } = \\ = \sqrt{ {3}^{2} - 2 \cdot 3 \cdot 2 \sqrt{3} + {(2 \sqrt{3} )}^{2} } = \sqrt{ {(3 - 2 \sqrt{3} )}^{2} } \\ = |3 - 2 \sqrt{3} | = 2 \sqrt{3} - 3[/tex]
→
[tex]m_{a} = \frac{x + y}{2} = \\ = \frac{2 \sqrt{3} + 3 + 2 \sqrt{3} - 3}{2} = \frac{4 \sqrt{3} }{2} = 2 \sqrt{3}[/tex]
[tex]m_{g} = \sqrt{xy} = \sqrt{(2 \sqrt{3} + 3)(2 \sqrt{3} - 3)} = \\ = \sqrt{{(2 \sqrt{3} )}^{2} - {3}^{2} } = \sqrt{12 - 9} = \sqrt{3} [/tex]
