Question

Cu cat este egala media aritmetica si media geometrica  a numerelor x,y daca:
a) x= $[5,(6)- \frac{15}{4} +0.75] * \frac{3}{2}$ si  y= $(\frac{1}{12} ) ^{-1} + \sqrt{116,64} : \frac{27}{10}$
b) x=$( 3 \frac{3}{5} ) ^{-1} + \sqrt{0,8(3)*0,0(3)}$ si y=$\frac{7}{ 2\sqrt{3} } * [0,125-0,25 +(-1) ^{-8} ] ^{-1}$

Answer 1

a) x=  si  y= 
5,(6)=56-5/9=51/9 simplificam=17/3
0,75=75/100 simplificam=3/4
x=(17/3-15/4+3/4)·3/2=(17/3-12/4)·3/2=(17/3-3)·3/2=8/3·3/2=4
deci x=4
(1/12) la puterea -1=12
√116,64=10,8=108/10 
y=12+108/10:27/10=12+108/10·10/27=12+4=16
y=16
Ma=x+y/2
Ma=4+16/2=20/2=10
Mg=√xy
Mg=√4·16=2·4=8
b) x= si y=
(33/5)la puterea -1=(3·5+3)/5 totul la puterea -1=(18/5) la puterea -1=5/18
0,8(3)=83-8/90=75/90 simplificam=5/6
0,0(3)=3/90 simplficam=1/30
x=5/18+√5/6·1/30=5/18+√5/180=5/18+√1/36=5/18+1/6=8/18 simplificam=4/9
deci x=4/9
7/2√3=rationalizam=14√3/12
0,125=125/1000 simplificam=1/8
0,25=25/100 simplificam=1/4
(-1) la puterea -8=1/(-1)la puterea 8=1/1=1
y=14√3/12·(1/8-1/4+1)la puterea -1=14√3/12·(7/8)la puterea -1=14√3/12·8/7= simplificam=4√3/3
y=4√3/3
Ma=(4/9+4√3/3)/2=16√3/18 simplificam=8√3/9
Mg=√4/9·4√3/3=16√3/27