Question

Solve the equation using any technique x^2 =3x-1

Answer 1

Answer:

The solutions to the quadratic equation are:

$x=\frac{3+\sqrt{5}}{2},\:x=\frac{3-\sqrt{5}}{2}$

Step-by-step explanation:

Consider the provided equation.

$x^2 =3x-1$

Add 1 and subtract 3x from both sides.

$x^2-3x+1 =0$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute the value of a=1, b=-3 and c=1 in above formula.

$x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}$

$x_{1,\:2}=\frac{3\pm\sqrt{5}}{2}$

Hence, the solutions to the quadratic equation are:

$x=\frac{3+\sqrt{5}}{2},\:x=\frac{3-\sqrt{5}}{2}$

Answer 2

X=2.6 there is more but it really does not matter