Question

Subiectul al III-lea (30 puncte) 4 (15p) 1. Calculați: √27 3 5 2√12 6√3 (15p) 2. Calculați: √34-24-√² + 5√2 6 8 √96 18 16) + 2√/6 (√8-√12). √216​

Answer 1

Răspuns:

Explicație pas cu pas:

1. (4/√27+3/2√12-5/6√3):5√2/6=(4/3√3+3/4√3-5/6√3)·6/5√2=

(4√3/9+3√3/12-5√3/18)·6/5√2=[(4·4√3+3·3√3-5·2√3)/36]·6/5√2=

[(16√3+9√3-10√3)/36]·6/5√2=(15√3/36)·6/5√2=(15√3·6)/36·5√2=  

15√3/6·5√2=3√3/6√2=√3/2√2=√3·√2/4=√6/4

2. √3(9/√54-4/√24)-√2(8/√96-18/√216)+1/2√6(√8-√12)=

√3(9/3√6-4/2√6)-√2(8/4√6-18/6√6)+1/2√6(2√2-2√3)=

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

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

1/√2+1/√3+1/√3-1/√2=2/√3=2√3/3