Question

${x}^{2} - 4x + 1 = 0$
Please solve this equation.
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Answer 1

x^2 - 4x + 1 = 0

we can also write

x^2 - 4x + 4 - 4 + 1= 0

(x - 2)^2 - 3 = 0

(x - 2)^2 - sqrt3^2=0

(x - 2 - sqrt3)(x -2 + sqrt3)=0

x = 2 + sqrt3 and 2 - sqrt3

formula used

A^2 - B^2 = (A + B)(A - B)

Answer 2

${x}^{2} - 4x = - 1$

${x}^{2} - 4x + 2 = - 1 + 2$

${(x - 2)}^{2} = 1$

$x - 2 = \sqrt{1}$

$x - 2 = 1$

$x = 1 + 2$

$x = 3$

Used Completing the Square method