Question

Se sabe que a³+ b³ = 20 y a+b = 5 , ¿cual es el valor de “a.b”? a)5 b)7 c)25 d)14 e)9​

Answer 1

Explicación paso a paso:

${a}^{3} + {b}^{3} = 20 \\ a + b = 5 \\ b = 5 - a \\ {a}^{3} + ( {5 - a)}^{3} = 20 \\ {a}^{3} + 125 - 3(25)(a) + 3(5)( {a)}^{2} - {a}^{3} = 20\\ 125 - 75a + 15( {a)}^{2} = 20 \\ 15 {a}^{2} - 75a + 125 - 20 = 0 \\ 15 {a}^{2} - 75a + 105 = 0 \\ {a}^{2} - 5a + 7 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2 } - 4ac } }{2a} \\ x = \frac{ - ( - 5) + - \sqrt{ {( - 5}^{2} - 4(1)(7 } }{2(1)} \\ \\ x = \frac{5 + - \sqrt{25 - 28} }{2} \\ x = \frac{5 + - \sqrt{ - 3} }{2} \\ x = \frac{5 + \sqrt{ - 3} }{2}$