Question

Rezolvati in numere reale ecuatia:
$\frac{1}{x}$-$\frac{x}{4}$=1 ,x diferit de 0

Answer 1

$\frac{1}{x}- \frac{x}{4}=1$
$\frac{4- x^{2}}{4x}= 4x=\ \textgreater \ 4- x^{2} =4x$×4x⇒
⇒4-x²=16x²
⇒4=16x²+x²
⇒17x²=4 |÷17
⇒x²=$\frac {4}{17}$
⇒x=$\sqrt \frac{4}{17}$
⇒x=$\frac{2}{ \sqrt{17} }$
⇒x=$\frac{2 \sqrt{17} }{17}$