Question

a+b=5
a • b=2
Calculați:
a) a pătrat + b pătrat
b) |a-b|
c) a la a 3 a + b la a 3 a

Answer 1

Explicație pas cu pas:

a)a+b=5 =>(a+b)²=25 => a²+2ab+b²=25 => a²+2×2+b²=25 => a²+b²=21

b)a²-2ab+b²=a²+b²-2ab=21-2×2=21-4=17

(a-b)²=17 => a-b=V17 sau -V17

=>|a-b|=V17

c) a+b=5 => (a+b)³=125 => a³+2a²b+b²a+ba²+2ab²+b³=125 => a³+2×a×ab+b×ba+ba×a+2ab×b+b³=125

a³+4a+2b+4b+2a+4b+b³=125

a³+b³+4(a+b)+2(a+b)=125

a³+b³+4×5+2×5=125

a³+b³+30=125 => a³+b³=95