Question

vă rog să mă ajutați la acest exercițiu!!​

Answer 1

Răspuns:

Explicație pas cu pas:

a) (√54-12/2√6)+(48/√6-30/4√6-2/√24)=

(3√6-6/√6)+(48/√6-15/2√6-2/2√6)=

(3√6-6√6/6)+(48√6/6-15√6/12-2√6/2·6)=(3√6-√6)+(8√6-15√6/12-√6/6)=

10√6-5√6/12-√6/6=(12·10√6-5√6-2√6)/12=(120√6-7√6)/12=103√6/12

b) (9/√3-12/√12+14/2√3)-(8√3-8/√27+15/2√3)=

(9/√3-12/2√3+14/2√3)-(8√3-8/3√3+15/2√3)=

(9√3/3-12√3/2·3+14√3/2·3)-(8√3-8√3/3·3+15√3/2·3)=

(3√3-2√3+7√3/3)-(8√3-8√3/3·3+5√3/2)=

(√3+7√3/3)-(8√3-8√3/9+5√3/2)=

(3√3+7√3)/3-(8·18√3-8·2√3+5·9√3)/18=

10√3/3-(144√3-16√3+45√3)/18=10√3/3-173√3/18=(6·10√3-173√3)/18=

(60√3-173√3)/18=-113√3/18

c) (9/√27-3/√3+2/√12)-(√12-45/√75+48/4√12)=

(9/3√3-3/√3+2/2√3)-(2√3-45/5√3+48/4·2√3)=

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

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