Question

dau 47 de puncte si coroana
imaginea de mai jos

Answer 1

1)
a+b= 3/4
a/b=3/4 = k ⇒ a=3k si b=4k
3k+4k=3/4 ⇒ 7k=3/4⇒ k=3/28
a=3*3/28=9/28
b=4*3/28=12/28

Media aritmerica = (a+b) :2= 3/4 :2/1= 3/4 * 1/2=3/8
Media geometrica = √ab = √(9/28*12/28) = 3*2√3/28=6√3/28= 3√3/14

2)
x+y=2/5
x/y=2/5 = k⇒ x=2k si y=5k
2k+5k=2/5
7k=2/5⇒ k=2/35
x=2*2/35=4/35
y=5*2/35=10/35

Media aritmetica = (x+y):2=2/5:2/1=2/5*1/2=1/5
Media geometrica= √(4/35*10/35) = 2*√10/35

Answer 2

13). a/b = 3/4, de unde a = 3b/4
a+b=3/4, inlocuim pe a in functie de b:
3b/4 + b = 3/4, se aduce la acelasi numitor:
3b + 4b = 3, rezulta b = 3/7
a = 3/7 * 3/4 = 9/28
Media aritmetica = (3/7 + 9/28) ÷ 2 = 3/4 ÷ 2 = 3/8.
Media geometrica = √(9/28 * 3/7) = √(21/196) = √21 / 14.

14). c/d = 2/5, de unde c = 2d/5
c+d=2/5, inlocuim pe c in functie de d:
2d/5 + d = 2/5, se aduce la acelasi numitor:
7d=2, rezulta d=2/7
c = 2/7 * 2/5 = 4/35
Media aritmetica = (2/7 + 4/35) ÷ 2 = 2/5 ÷ 2 = 2/10 = 1/5
Media geometrica = √(4/35 * 2/7) = √(8/245) = 2√2 / 7√5 = 2√10 / 35