Question

find the value of x
${x}^{2} - 4x + 1$

Answer 1

HEYA MATE, HERE IS UR ANSWER


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


By middle term splitting

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

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

x (x-2)+1 (-2x+1)

(x+1)(x-2)

x+1=0
x=-1

x-2=0
x=2


$\huge\boxed {\mathbb{BE\:BRAINLY}}$

Answer 2

Solving x2-4x+1 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC
x = ————————
2A

In our case, A = 1
B = -4
C = 1

Accordingly, B2 - 4AC =
16 - 4 =
12

Applying the quadratic formula :

4 ± √ 12
x = —————
2

Can √ 12 be simplified ?

Yes! The prime factorization of 12 is
2•2•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 12 = √ 2•2•3 =
± 2 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321
So now we are looking at:
x = ( 4 ± 2 • 1.732 ) / 2

Two real solutions:

x =(4+√12)/2=2+√ 3 = 3.732

or:

x =(4-√12)/2=2-√ 3 = 0.268

i hope its hlp you