Question

Cum se rezolva 1 si 2?

Answer 1

1)
a+b=10 (a+b)²=10²  a²+2ab+b²=100    a²+b²=100-2ab   a²+b²=100-2=98
ab=1
a³+b³=(a+b)(a²-ab+b²)=10×(98-1)=970

2
a/b=√3      a=b√3
(a²-ab+2b²)/(2a²-ab+b²) =
=[(b√3)²-b×b√3+2b²)]/[2(b√3)²-b×b√3+b²)=
=(3b²-b²√3+2b²)/(6b²-b²√3+b²)=
=(5b²-b²√3)/(7b²-b²√3)=
=b²(5-√3)/b²(7-√3)=
=(5-√3)/(7-√3)=
=(5-√3)(7+√3)/(7-√3)(7+√3)=
=(35-7√3+5√3-3)/(49-3)=
=(32-2√3)/46=
=(16-√3)/23