Question

sabendo que a+b=7 e a.b=3 valor de:

A) a²+b²

B)a³+b³

Answer 1

a + b = 7
ab = 3
a² + b²
a³ + b³
( a + b)² = 7²
a² +2ab + b² = 49
(a² + b² ) + 2ab = 49
( a² + b²) + 2(3) = 49
a² + b² + 6 = 49
a² + b²= 49 - 6
a² + b² = 43 ****

b
a³ + b³  = ( a + b) ( a² -ab + b² )
substituindo  a + b = 7
a³ + b³ =(a² - ab + b²  ) ( 7 ) 
a³ + b³  = ( a² + b²) - ab ] 7  =
a³ + b³ = (43 - 3 ).7
a³ + b³ = 40 * 7
a³ + b³ = 280 ***