X²-4x+3=0, then what is the value of (x-2)²=?

Question

asked Oct 12, 2021 95.6k views

1 Answer

Omar Magdy · Answer 1 · 2021-10-18T18:17:37+0000

Answer:

We conclude that:

$\left(x-2\right)^2=1$

Explanation:

Given the expression

x^2-4x+3=0

subtract 3 from both sides

x^2-4x+3-3=0-3

x^2-4x=-3

Add -2² to both sides

$x^2-4x+\left(-2\right)^2=-3+\left(-2\right)^2$

simplify

$x^2-4x+\left(-2\right)^2=1$

Applying the perfect square formula: (a-b)² = a²-2ab+b²

so

$\left(x-2\right)^2=1$ ∵
$x^2-4x+\left(-2\right)^2=\left(x-2\right)^2$

Therefore, we conclude that:

$\left(x-2\right)^2=1$