Question

Se x é um numero real tal que √2x-1=x determine o valor de x :

Answer 1

$\sqrt{2x-1}=x\to \\\\ ( \sqrt{2x-1} )^2=(x)^2\to\\\\2x-1=x^2\to\\\\\\ x^2-2x+1=0\\\\ a=1;b=-2;c=1\\\\\\ \Delta=b^2-4ac\to \Delta=(-2)^2-4*1*1\to \Delta=4-4\to \Delta=0\\\\ x'=x'' \\\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-2)\pm \sqrt{0} }{2*1} \to x= \frac{2\pm 0 }{2} \to \\\\\\ x'=x''= \frac{2 }{2} \to x'=x'' =1\\\\\\\\ S= \{1\}$

$\sqrt{2x-1} =x\to \sqrt{2*1-1} =1\to \sqrt{2-1} =1\to \sqrt{1} =1\to 1=1$


R.: x=1