Question

Hallar: N= a^2+a^3+b^2+b^3 si: ab=12 y a+b=7​

Answer 1

Respuesta:

$n = a {}^{2} + {b}^{2} + {a}^{3} + {b}^{3} \\ ab = 12 \: \: \: \: a + b = 7 \\ (a + b) {}^{2} = {a}^{2} + b {}^{2} + 2ab \\ {7}^{2} - 24 = a {}^{2} + b {}^{2} \\ a {}^{2} + b {}^{2} = 25 \\ \\ (a + b) {}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ 7 {}^{3} = a {}^{3} + {b}^{3} + 3(12)(7) \\ 343 - 252 = {a}^{3} + b {}^{3} \\ a {}^{3} + b {}^{3} = 91 \\ n = 25 + 91 \\ n = 116$