Question

Calculati: a) (√54-12/2√6)+(48/√6-4√6-2/√24)=
b) (9/√3-12/√12+14/2√3)-(8√3-8/√27+15/2√3)=
c) (9/√27-3/√3+2/√12)-(√12-45/√75+48/4√12)=
d) (5/√2-3/2√2)-(5√2/6+7/3√2+18/√18)=

Va rog ajutati-ma . Multumesc

Answer 1

a) (√54-12/2√6)+(48/√6-4√6-2/√24)=
=(3√6-6/√6)+(48/√6-4√6-2/2√6)=
=(3√6-6√6/6)+(48√6/6-4√6-√6/6)=
=3√6-√6+8√6-4√6-√6/6=
=6√6-√6/6=
=(36√6-√6)/6=
=35√6/6


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√3/3-6√3/3+7/√3)-(8√3-8√3/9+15√3/6)=
=(3√3-2√3+7√3/3)-(8√3-8√3/9+5√3/2)=
=(42√3-126√3+16√3-45√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+48/8√3)=
= (3/√3-3/√3+1/√3)-(2√3-9/√3+6/√3)=
= 1/√3-2√3+3√3/3=
= 1/√3-2√3+√3=
= √3/3-√3=
= (√3-3√3)/3=
=-2√3/3


d) (5/√2-3/2√2)-(5√2/6+7/3√2+18/√18)=
 =(5√2/2-3√2/4)-(5√2/6+7√2/6+18/3√2)=
 =(5√2/2-3√2/4)-(5√2/6+7√2/6+6√2/2)=
 =5√2/2-3√2/4-5√2/6-7√2/6-3√2)=
 =(30√2-9√2-10√2-14√2/6-36√2)/12=
 =(30√2-9√2-10√2-14√2-36√2)/12=
=-41√2/12