Answer:
The solutions to the quadratic equation are:
[tex]x=\frac{3+\sqrt{5}}{2},\:x=\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]x^2 =3x-1[/tex]
Add 1 and subtract 3x from both sides.
[tex]x^2-3x+1 =0[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute the value of a=1, b=-3 and c=1 in above formula.
[tex]x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{3\pm\sqrt{5}}{2}[/tex]
Hence, the solutions to the quadratic equation are:
[tex]x=\frac{3+\sqrt{5}}{2},\:x=\frac{3-\sqrt{5}}{2}[/tex]
