Đáp án:
`S = {`$\dfrac{1 +\sqrt{51}}{5}; \dfrac{1 -\sqrt{51}}{5}$`}`
Giải thích các bước giải:
`5x² -2x -10 = 0`
$⇔ (\sqrt{5}x)² -2.\sqrt{5}x.\dfrac{\sqrt{5}}{5} +(\dfrac{\sqrt{5}}{5})² -(\dfrac{\sqrt{5}}{5})² -10 = 0$
$⇔ (\sqrt{5}x -\dfrac{\sqrt{5}}{5})²$ `-51/5 = 0`
$⇔ (\sqrt{5}x -\dfrac{\sqrt{5}}{5} -\sqrt{\dfrac{51}{5}}).(\sqrt{5}x -\dfrac{\sqrt{5}}{5} +\sqrt{\dfrac{51}{5}}) = 0$
$⇔ \left[ \begin{array}{l}\sqrt{5}x -\dfrac{\sqrt{5}}{5} -\sqrt{\dfrac{51}{5}} = 0\\\sqrt{5}x -\dfrac{\sqrt{5}}{5} +\sqrt{\dfrac{51}{5}}=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=\dfrac{1 +\sqrt{51}}{5}\\x=\dfrac{1 -\sqrt{51}}{5}\end{array} \right.$
Vậy `S = {`$\dfrac{1 +\sqrt{51}}{5}; \dfrac{1 -\sqrt{51}}{5}$`}`
