Question

Calculati: ( va rogg exercitiul din imagine) ​

Answer 1

Răspuns:

Explicație pas cu pas:

a) √2(4/√18+√0,(2))+√3(√0,(3)+2/√3)=

√2[4/3√2+√(2/9)]+√3[√(3/9)+2/√3]=

4√2/3√2+√2√2/3+√3·1/√3+2√3/√3= 4/3+2/3+1+2=6/3+3=2+3=5

b) √5(5/3√5+ √0,(5)+√20/6)-√6(√0,(6)+2√2/√3)=    

√5[5/3√5+ √(5/9)+2√5/6]-√6[√(6/9)+2√2/√3]=

5√5/3√5+5/3+2·5/6-6/3-2√12/√3=5/3+5/3+5/3-2-4=15/3-6=5-6=-1

c) (14/3√7-15/2√175)+(3√28/4-2/√63)+(√7/2-14/√28)=                    

(14/3√7-15/2·5√7)+(3·2√7/4-2/3√7)+(√7/2-14/2√7)=                

(14/3√7-3/2√7)+(3√7/2-2/3√7)+(√7/2-7/√7)=

14√7/21-3√7/14+3√7/2-2√7/21+√7/2-7√7/7=

2√7/3-3√7/14+3√7/2-2√7/21+√7/2-√7=

√7(2/3-3/14+3/2-2/21+1/2-1)= √7(2·14-3·3+3·21-2·2+1·21-1·42)/42=

√7(28-9+63-4+21-42)/42=57√7/42

d) 6√20/7√5(3/2√54+√0,1(6)-5/√6)=

6·2√5/7√5[3/2·3√6+√(15/90)-5/√6]=6/7(1/2√6+1/√6-5/√6)=

6/7(1/2√6-4/√6)=6/7·(1-2·4)/√6=6/7·(-7)/√6=6·(-7)/7√6=-6/√6=

-6√6/6=-√6