Question

Rezolvati in R ecuatia:
√2x+3= x

Answer 1

[tex]x= \sqrt{2}x+3 /- \sqrt{2}x \\ x- \sqrt{2}x=3 \\ x(1- \sqrt{2} )=3 /:(1- \sqrt{2} ) \\ x= \frac{3}{1- \sqrt{2} } \\ [/tex]

Rationalizăm, amplificând fracția cu $(1+ \sqrt{2} )$ 
$x= \frac{3(1+ \sqrt{2} )}{(1- \sqrt{2} )(1+ \sqrt{2} )} \\ x= \frac{3(1+ \sqrt{2} )}{ 1^{2} -( \sqrt{2}^{2} )} \\ x= \frac{3(1+ \sqrt{2} )}{1-2} \\ x= \frac{3(1+ \sqrt{2} )}{-1} \\ x=-3(1+ \sqrt{2} )$

Observ că nu se vede ok prima parte. 
$x= \sqrt{2}x+3 / - \sqrt{2}x \\ x- \sqrt{2}x=3 \\ x(1- \sqrt{2} )=3 /:(1- \sqrt{2} ) \\ x= \frac{3}{1- \sqrt{2} }$