Question

x²-2x+1=7 calculeaza ecuatia

Answer 1

x² -2x  +1 - 7 = 0 
x² -2x -6 =0 
Δ = 4 - 4 ·( -6 ) = 4 + 24 = 28            ; √Δ= √28 = √4·√7 = 2√7
x₁ = ( 2 - √28 ) /2 = ( 2 -2 √7 ) /2 = 1 - √7 
x₂ = 1 + √7

Answer 2

$x^2-2x+1=7 \\ x^2-2x=7-1 \\ x^2-2x=6 \\ x^2-2x-6=0 \\ a=1,b=-2,c=-6$
Δ $=b^2-4ac=2^2-4*1*(-6)=4+24=28\ \textgreater \ 0$
$x_1= \frac{2+ \sqrt{28} }{2*1} = \frac{2+2 \sqrt{7} }{2} = \frac{2(1+ \sqrt{7} )}{2} =1+ \sqrt{7} \\ x_2= \frac{2- \sqrt{28} }{2*1} = \frac{2-2 \sqrt{7} }{2} = \frac{2(1- \sqrt{7}) }{2} =1- \sqrt{7} \\ S= \left \{ 1- \sqrt{7} ;1+ \sqrt{7} \left \}$