Question

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

Answer 1

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`