Question

calculati media aritmetica si media geometrica a numerelor : x= 7 radical 8 - radical50. si y= 3radical32 - radical72​

Answer 1

x = 7√8 - √50 = 2·7√2 - 5√2 = (14 - 5)√2 = 9√2

y = 3√32 - √72 = 3·4√2 - 6√2 = (12√2 - 6√2) = 6√2

Ma = (x + y)/2 = (9√2+6√2)/2 = 15√2/2

Mg = √x·y = √9√2·6√2 = √54·2 = √108 = √2²·3³ = 6√3

Answer 2

Răspuns:

$x = 7\sqrt{8} - \sqrt{50}, y = 3\sqrt{32} - \sqrt{72}$

$x = 7\sqrt{2^{3}} - \sqrt{2 * 5^{2}}, y = 3\sqrt{2^{5}} - \sqrt{2^{3} * 3^{2}}$

$x = 7 * 2\sqrt{2} - 5\sqrt{2}, y = 3 * 4\sqrt{2} - 2 * 3\sqrt{2}$

$x = 14\sqrt{2} - 5\sqrt{2}, y = 12\sqrt{2} - 6\sqrt{2}$

$x = 9\sqrt{2}, y = 6\sqrt{2}$

Media aritmetica: $\frac{9\sqrt{2} + 6\sqrt{2}}{2} = \frac{15\sqrt{2}}{2}$

Media geometrica: $\sqrt[2]{9\sqrt{2} * 6\sqrt{2}} = \sqrt[2]{9 * 6 * 2} = \sqrt[2]{54 * 2} = \sqrt[2]{108} = \sqrt[2]{2^{2} * 3^{3}} = 2 * 3\sqrt{3} = 6\sqrt{3}$

Explicație pas cu pas: