Question

9. Calculati media geometrica si media aritmetica a numerelor:
(Ex in poza)

100p + coroana

Answer 1

Răspuns:

Explicație pas cu pas:

9. Calculati media geometrica si media aritmetica a numerelor:

a) x=√(2√5-6)²=| 2√5-6 |=6-2√5

y=√(2√5+6)²=| 2√5+6 |=2√5+6

media geometrica=√(x·y)=√(6-2√5)(6+2√5)=√(36-4·5)=√16=4

media aritmetica=(x+y)/2=(6-2√5+6+2√5)/2=12/2=6

b) x=√(√3-√5)²+√3+3=| √3-√5 |+√3+3=√5-√3+√3+3=√5+3

y=√(√5-2√2)²-√8-(-3)=| √5-2√2 |-2√3+3=-(√5-2√2)-2√3+3=

-√5+2√2-2√2+3=3-√5

media geometrica=√(x·y)=√(3+√5)(3-√5)=√(9-5)=√4=2

media aritmetica=(x+y)/2=(√5+3+3-√5)/2=6/2=3

c) x=72√6(1/2√2-1/4√2)=72√6/2√2-72√6/4√2=36√(6/2)-18√(6/2)=

36√3-18√3=18√3

y=√3+(1-√3)(3+√3)/6=√3+(3+√3-3√3-3)/6=√3-2√3/6=√3-√3/3=

(3√3-√3)/3=2√3/3

media geometrica=√(x·y)=√(18√3·2√3/3)=√(18·2·3/3)=√36=6

media aritmetica=(x+y)/2=(18√3+2√3/3)/2=[(54√3+2√3)/3]/2=56√3/6=28√3/3

d) x=| √11-4 | +√(4+√11)²+10=4-√11+ | 4+√11 | +10=4-√11+4+√11+10=18

y=| 2√2-3 | -√(3+2√2)²+√32+√(-8)²=-(2√2-3)-| 3+2√2 |+4√2+| -8 |=

-2√2+3-3-2√2+4√2+8=8

media geometrica=√(x·y)=√(18·8)=√144=√12²=12

media aritmetica=(x+y)/2=(18+8)/2=26/2=13