Question

4x²-4x+1=5 calculeaza ecuatia:

Answer 1

$4x^2-4x+1=5 \\ \\ (2x-1)^2=5 \Rightarrow 2x-1 = \pm \sqrt{5} \\ \\ 2x-1= \sqrt{5} \Rightarrow \boxed{x= \frac{ \sqrt{5}+1}{2} } \\ \\ 2x-1=- \sqrt{5} \Rightarrow \boxed{x= \frac{- \sqrt{5}+1}{2} }$

Answer 2

$4x^2-4x+1=5 \\ 4x^2-4x=5-1 \\ 4x^2-4x=4 \\ 4x^2-4x-4=0 \\ a=4,b=-4,c=-4$
Δ $=b^2-4ac=4^2-4*4*(-4)=16+64=80\ \textgreater \ 0$
$x_1= \frac{4+ \sqrt{80} }{2*4} = \frac{4+4 \sqrt{5} }{8} = \frac{4(1+ \sqrt{5} )}{8} = \frac{1+ \sqrt{5} } {2} \\ x_2= \frac{4- \sqrt{80} }{2*4} = \frac{4-4 \sqrt{5} }{8} = \frac{4(1- \sqrt{5} )}{8} = \frac{1-\sqrt{5} }{2} \\ S= \left \{ \frac{1+ \sqrt{5} }{2} ; \frac{1- \sqrt{5} }{2} \left \}$