Question

As dori o rezolvare la aceate exercitii, sunt cam blocat. Multumesc ^^​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 5/√6+5√2/√27-(4√3/√8-7√2/3√3)=

5/√6+5√2/3√3-(4√3/2√2-7√2/3√3)=

5√6/6+5√6/9-(4√6/4-7√6/9)=5√6/6+5√6/9+7√6/9-√6=

5√6/6+12√6/9-√6=5√6/6+4√6/3-√6=(5√6+8√6-6√6)/6=7√6/6

b) (√0,(3)+3/√12+√3/2)·√3-(√0,(6)+√24/3)·√6=

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

[√(1/3)+3/2√3+√3/2)·√3-[√(2/3)+2√6/3)·√6=

√(3/3)+3√3/2√3+√3·√3/2-[√(2·6/3)+2·√6·√6/3]=√1+3/2+3/2-[√4+2·6/3]=

1+3-(2+4)=4-6=-2

c) [(√6-√5)/√30+(√8-√6)/√48+(√9-√8)/√72]:√45/(3√5+5)=

[√6/√30-√5/√30+√8/√48-√6/√48+√9/√72-√8/√72]:√45/(3√5+5)=

[√(1/5)-√(1/6)+√(1/6)-√(1/8)+√(1/8)-√(1/9)]:√45/(3√5+5)=

[√(1/5)-√(1/9)]:√45/(3√5+5)=[√(1/5)-√(1/9)]·(3√5+5)/√45=

=[√(1/5)-√(1/9)]·(3√5+5)/3√5=(3√5+5)/√5·3·√5-(3√5+5)/3·3√5=

(3√5+5)/15-(3√5+5)/9√5=(3√5+5)/15-(3√5+5)√5/9√5·√5=

(3√5+5)/15-(15+5√5)/45=[3(3√5+5)-(15+5√5)]/45=(9√5+15-15-5√5)/45=

4√5/45