Question

calculati media aritmetica a nr reale x si y daca:​

Answer 1

media aritmetica a nr x,y= (x+y)÷2

$a) \frac{2 \sqrt{3} + \sqrt{18} + 5 \sqrt{12} - \sqrt{2} }{2} = \\ \frac{2 \sqrt{3} + 3 \sqrt{2} + 5 \times 2 \sqrt{3} - \sqrt{2} }{2} = \\ \frac{2 \sqrt{3} + 2 \sqrt{2} + 10 \sqrt{3} }{2} = \\ \frac{12 \sqrt{3} + 2 \sqrt{2} }{2} = \\ 6 \sqrt{3} + \sqrt{2}$

$b) \frac{ \sqrt{63} - 5 \sqrt{3} + 3 \sqrt{27} - \sqrt{7} }{2} = \\ \frac{3 \sqrt{7} - 5 \sqrt{3} + 3 \times 3 \sqrt{3} - \sqrt{7} }{2} = \\ \frac{2 \sqrt{7} - 5 \sqrt{3} + 9 \sqrt{3} }{2} = \\ \frac{2 \sqrt{7} + 4 \sqrt{3} }{2} = \\ \sqrt{7} + 2 \sqrt{3}$

$c) \frac{2 \sqrt{2} + \sqrt{45} + 2 \sqrt{50} - \sqrt{5} }{2} = \\ \frac{2 \sqrt{2} + 3 \sqrt{5} + 2 \times 5 \sqrt{2} - \sqrt{5} }{2} = \\ \frac{2 \sqrt{2} + 10 \sqrt{2} + 2 \sqrt{5} }{2} = \frac{12 \sqrt{2} + 2 \sqrt{5} }{2} = \\ 6 \sqrt{2} + \sqrt{5}$