<PRE><B>Question 122621</B>
find an equation with coefficients whose roots are 2 plus and minus the square root of 3 divided by 3
:
x = {{{(2+-sqrt(3))/3}}}
:
Multiply both sides by 3:
3x = {{{2+-sqrt(3)}}}
:
Subtract 2 from both sides
3x - 2 = +/-{{{sqrt(3)}}}
:
Square both sides:
(3x-2)^2 = 3
:
FOIL
9x^2 - 12x + 4 = 3
:
Subtract 3 from both sides:
9x^2 - 12x + 4 - 3 = 0
:
9x^2 - 12x + 1 = 0 is our equation </PRE>