calculati x+y si x-y, unde: a) x=3√150(6√98-8√50-7√108+10√48) y=4√54(3√192-8√72-4√75+11√32) b) x= 5√24(4√192-3√432+3√243-5√75) y=3√216(3√72-4√162+6√200-5√128) plzzzz cine mă ajuta
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
calculati x+y si x-y, unde:
a) x=3√150·(6√98-8√50-7√108+10√48)=
3·5√6·(6·7√2-8·5√2-7·6√3+10·4√3)=
15√6·(42√2-40√2-42√3+40√3)=
15√6·(2√2-2√3)=15√6·2·(√2-√3)=30√6(√2-√3)=30√12-30√18=
30·2√3-30·3√2=30(2√3-3√2)
y=4√54(3√192-8√72-4√75+11√32)=4·3√6·(3·8√3-8·6√2-4·5√3+11·4√2) =12√6·(24√3-48√2-20√3+44√2)=12√6·(4√3-4√2)=12·4√6(√3-√2)=
48√18-48√12=48·3√2-48·2√3=48(3√2-2√3)
x+y=30(2√3-3√2)+48(3√2-2√3)=60√3-90√2+144√2-96√3=54√2-36√3
x-y=30(2√3-3√2)-48(3√2-2√3)=60√3-90√2-144√2+96√3=
=156√3-234√2
b) x= 5√24(4√192-3√432+3√243-5√75)
=5·2√6·(4·8√3-3·12√3+3·9√3 -5·5√3)=10√6·(32√3-36√3+27√3-25√3)
=10√6·(-2√3)=-20√18=-20·3√2=-60√2
y=3√216(3√72-4√162+6√200-5√128)=
3·6√6·(3·6√2-4·9√2+6·10√2-5·8√2)=
18√6·(18√2-36√2+60√2-40√2)=18√6·(2√2)=36√12=72√3
x+y=-60√2+72√3
x-y=-60√2-72√3