Answer:
We conclude that:
[tex]\left(x-2\right)^2=1[/tex]
Step-by-step explanation:
Given the expression
[tex]x^2-4x+3=0[/tex]
subtract 3 from both sides
[tex]x^2-4x+3-3=0-3[/tex]
[tex]x^2-4x=-3[/tex]
Add -2² to both sides
[tex]x^2-4x+\left(-2\right)^2=-3+\left(-2\right)^2[/tex]
simplify
[tex]x^2-4x+\left(-2\right)^2=1[/tex]
Applying the perfect square formula: (a-b)² = a²-2ab+b²
so
[tex]\left(x-2\right)^2=1[/tex] ∵ [tex]x^2-4x+\left(-2\right)^2=\left(x-2\right)^2[/tex]
Therefore, we conclude that:
[tex]\left(x-2\right)^2=1[/tex]
