Respuesta :

X= -b +- square root of b^2-4ac
——————-
2a

6 +- square root of 36-4(2)(1)
———
4

6+- square root of 32
———
4

6+- 4 square root of 2
———
4

3 +- 2 square root of 2
———
2

Answer with Step-by-step explanation:

We have to solve the equation 2x²-6x+1=0

the solution of the equation ax²+bx+c=0 is given by

[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\ and\ x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

Here a=2,b=-6 and c=1

[tex]x=\dfrac{6+\sqrt{6^2-4\times 2\times 1}}{2}\ and\ x=\dfrac{6-\sqrt{6^2-4\times 2\times 1}}{2}\\\\x=\dfrac{6+\sqrt{36-8}}{2}\ and\ x=\dfrac{6-\sqrt{36-8}}{2}\\\\x=\dfrac{6+\sqrt{28}}{2}\ and\ x=\dfrac{6-\sqrt{28}}{2}\\\\x=\dfrac{6+2\sqrt{7}}{2}\ and\ x=\dfrac{6-2\sqrt{7}}{2}\\\\x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

Hence, solution of 2x²-6x+1=0 is:

[tex]x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

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