Răspuns:
Explicație pas cu pas:
a³+b³=(a+b)(a²+3a²b+3ab²+b²)=(a+b)[a²+b²+3ab(a+b)]
a²+b²=(a+b)²-2ab=5²-2·2=25-4=21
a³+b³=5·(21+3·2·5)=5·51=255
a^4+b^4=(a²+b²)²-2(ab)²=21²-2·2²=441-8=433
1/a+1/b=(a+b)/ab=5/2=2,5
1/a²+1/b²=(a²+b²)/a²b²=21/4=5,25
1/a³+1/b³=(a³+b³)/(ab)³=255/8=31,875
