Question

Calculati media geometrica a numerelor a si b si ordonati crescator numerele a, mg si b pentru:
a)a=2 si b=18
b)a=radical 12 si b=radical108
c)a=5 radical 3 si b=5 radical 3
d)a=1 supra 5 si b=0,8
e)a=7+4radical 3 si b=7-4 radical 3
f)a= 5radical 2-7 si b=7+5radical 2



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Answer 1

Răspuns:

Explicație pas cu pas:

a) a=2; b=18; mg=√(2·18)=√36=6. Ordonare:  2; 6; 18

b) a=√12; b=√108;   mg=√(a·b)=√(√12 ·√108) = √(√(12·108)) = √(√(12·12·9))=√(12·3)=√36=6.  Ordonare:  √12; 6; √108

c) a=5√3; b=5√3;   mg=√(5√3 ·5√3)=5√3. Ordonare:  5√3; 5√3;  5√3

d) a=1/5;  b=0,8;  mg=√a·b)=√(0,2·0,8)=√(0,16)=0,4

Ordonare:   1/5;  0,4;  0,8

a)  a=7+4√3;  b=7-4√3;   mg=√(a·b)=√( (7-4√3)(7+4√3) ) = √(7²-(4√3)²)=

=√(49-48)=√1=1.  Ordonare:  Verificam daca b<1

7-4√3 < 1. 7-1 < 4√3,   6 < 4√3,  ridicam la patrat,   6² < (4√3)²,  36 < 48 adevarat. Acum ordonarea:  7-4√3;  1;  7+4√3

f) a=5√2 -7;  b=7 +5√2;  mg=√(a·b)=√( (5√2 -7)(5√2+7) )= √( (5√2)²-7²)=

=√(50-49)=√1=1.  Verificam daca a<1

5√2 -7 <1,  5√2 < 8, rudicam la patrat,  (5√2)²<8²,   50 < 64 adevarat, deci ordonate:  5√2 -7 ;  1;  7+5√2