Question

Si a+b = 4 y ab = 4, calcula S = a² + b² + 4.​

Answer 1

Explicación paso a paso:

$ab = 4 \\ a = \frac{4}{b} \\ a + b = 4 \\ \frac{4}{b} + b = 4 \\ \frac{b}{1} \times \frac{b}{b} = \frac{ {b}^{2} }{b} \\ \frac{4}{b} + \frac{ {b}^{2} }{b} = 4 \\ \frac{4 + {b}^{2} }{b} = 4 \\ 4 + {b}^{2} = 4b \\ 4 + {b}^{2} - 4b = 0$

${b}^{2} - 4b + 4 = 0 \\ x = \frac{4 + - \sqrt{16 - 4 \times 4} }{2} \\ = \frac{4 + - \sqrt{0} }{2} = 2$

$b = 2 \\ a + b = 4 \\ a + 2 = 4 \\ a = 4 - 2 \\ a = 2$

$a = 2 \\ b = 2 \\ a + b = 2 + 2 = 4 \\ ab = 2 \times 2 = 4$

$s = {a}^{2} + {b}^{2} + 4 = \\ = {2}^{2} + {2}^{2} + 4 = \\ = 4 + 4 + 4 = 12$

espero te sirva