Question

Como resolver:

1/x+x=a

Me ajudem ?????

Answer 1

$\displaystyle \frac{1}{\text x}+\text x=\text a \\\\ \text{Multiplicando os dois lados por x} : \\\\ 1+\text x^2=\text {a.x} \\\\ \text x^2-\text a.\text x+1 = 0 \\\\ \text x =\frac{-(-\text a)\pm\sqrt{(-\text a)^2-4.1.1}}{2.1} \\\\\\ \text x = \frac{\text a\pm\sqrt{\text a^2-4}}{2} \\\\ \text{Portanto}: \\\\ \huge\boxed{\text x=\frac{\text a+\sqrt{\text a^2-4}}{2}\ \ ;\ \ \text x= \frac{\text a-\sqrt{\text a^2-4}}{2}}$

OBSERVAÇÃO:

Para que x pertença ao conjunto dos números reais, devemos ter Δ ≥ 0

$(-\text a)^2-4.1.1\geq 0 \\\\ \text a^2\geq 4\\\\ \text a \geq \pm \sqrt{4} \\\\ \huge\boxed{\text S =\{ \ \text a\in \mathbb{R} \ | \ \ 2 \leq \text a \leq -2 \ \} } \checkmark$