Question

9.Calculati media arimetrica si media geometrica a numarelor:
a)a=2-√3
b=2+√3
b)a-9+4√2
b=9-4√2

Answer 1

[tex]a. m _{a}= \frac{a+b}{2}= \frac{2- \sqrt{3}+2+ \sqrt{3} }{2}= \frac{4}{2}=2 \\ m_{g}= \sqrt{ab}= \sqrt{(2- \sqrt{3})(2+ \sqrt{3}) }= \sqrt{ 2^{2}- (\sqrt{3}) ^{2} }= \sqrt{4-3}= \sqrt{1}=1 \\ b. m_{a}= \frac{a+b}{2}= \frac{9+4 \sqrt{2}+9- 4\sqrt{2} }{2}= \frac{18}{2}=9 \\ m_{g}= \sqrt{(9+ 4\sqrt{2})(9- 4\sqrt{2}) }= \sqrt{ 9^{2}- (4\sqrt{2} )^{2} }= \sqrt{81-32}= \sqrt{49}=7[/tex]