Respuesta :

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A. x=3/2

D. x=1/2


Solve for x over the real numbers:

4 x^2 - 8 x + 3 = 0

The left hand side factors into a product with two terms:

(2 x - 3) (2 x - 1) = 0

Split into two equations:

2 x - 3 = 0 or 2 x - 1 = 0

Add 3 to both sides:

2 x = 3 or 2 x - 1 = 0

Divide both sides by 2:

x = 3/2 or 2 x - 1 = 0

Add 1 to both sides:

x = 3/2 or 2 x = 1

Divide both sides by 2:

Answer:  x = 3/2 or x = 1/2

Answer:

Hence, the correct options are A and D.

Step-by-step explanation:

[tex]4x^2-8x+3=0[/tex]

Splitting the term (-8x) by using middle term splitting theorem:

[tex]4x^2-2x-6x+3=0[/tex]

[tex]2x(2x-1)-3(2x-1)=0[/tex]

[tex](2x-1)(2x-3)=0[/tex]

[tex]2x-1=0[/tex]

[tex]x=\frac{1}{2}[/tex]

[tex](2x-3)=0[/tex]

[tex]x=\frac{3}{2}[/tex]

The solution of the given equation [tex]4x^2-8x+3=0[/tex] :

[tex]x=\frac{1}{2},\frac{3}{2}[/tex]

Hence, the correct options are A and D.