Question

La suma de 2 dígitos de un #primo es 11, y su producto 18 ¿El #es?​

Answer 1

Explicación paso a paso:

$a + b = 11 \\ ab = 18 \\ a = \frac{18}{b} \\ \\ a + b = 11 \\ \frac{18}{b} + b = 11 \\ \frac{18 + {b}^{2} }{b} = 11 \\ 18 + {b}^{2} = 11b \\ 18 + {b}^{2} - 11b = 0 \\ {b}^{2} - 11b + 18 = 0$

formula general

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a}$

$x = \frac{11 + - \sqrt{( - 11) {}^{2} } - 4 \times 1 \times 18 }{2 \times 1} = \\ = \frac{11 + - \sqrt{121 - 72} }{2} \\ = \frac{11 + - \sqrt{49} }{2} \\ x1 = \frac{11 + 7}{2} = \frac{18}{2} = 9 \\x2 = \frac{11 - 7}{2} = 2$

$a + b = 9 + 2 = 11 \\ ab = 9 \times 2 = 18$

espero te sirva