Question

Calculati media geometrica si media aritmetica pentru : 3 la puterea 13 si 3 la puterea 15 ,cu 10 la puterea-5 si 10 la put -7

Answer 1

med. aritm = (3¹³ + 3¹⁵ ) /2 = 3¹³· ( 1 + 3² ) /2 = 3¹³· ( 1 +9) /2 = 3¹³ ·10  / 2 =
                = 5· 3¹³
med. geom. = √3¹³3¹⁵ =√3¹³ ⁺¹⁵ =√ 3²⁸  = 3²⁸ /² = 3¹⁴

med. aritm = ( 10 ⁻⁵  + 10 ⁻⁷ ) /2 = 10⁻⁵· ( 1 + 10⁻²  ) /2 = 10 ⁻⁵ ·( 1 + 1 /100 ) ·1/2
                = 10⁻⁵· ( 100 + 1 ) / 100· 2 = 10⁻⁵ 101  / 10²· 2 = 10⁻⁷ · 101 / 2 
med. geom. = √ 10⁻⁵10⁻⁷= √ 10⁻⁵⁻⁶  = √10⁻¹²  = 10 ⁻¹²/ ² = 10⁻⁶