Answer: The required solution of the given quadratic equation is
x = 3 + √3 and x = 3 - √3.
Step-by-step explanation: We are given to solve the following quadratic equation using quadratic formula :
[tex]x^2-6x+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Quadratic formula : The solution of a quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given quadratic equation (i), we have
a = 1, b = -6 and c = 6.
Therefore, the solution of equation (i) is given by
[tex]x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-6)\pm\sqrt{(-6)^2-4\times 1\times6}}{2\times1}\\\\\\=\dfrac{6\pm\sqrt{36-24}}{2}\\\\\\=\dfrac{6\pm\sqrt{12}}{2}\\\\\\=\dfrac{6\pm2\sqrt{3}}{2}\\\\=3\pm\sqrt3.[/tex].
Thus, the required solution of the given quadratic equation is
x = 3 + √3 and x = 3 - √3.
