Question 1143178

{{{ (x+1)(x^2 + 1)(x^3 + 1)=30x^3}}}

{{{ (x^3 + x^2 + x + 1)(x^3 + 1)=30x^3}}}

{{{ x^6 + x^5 + x^4 + 2 x^3 + x^2 + x + 1=30x^3}}}

{{{ x^6 + x^5 + x^4 + 2 x^3 + x^2 + x + 1-30x^3=0}}}

{{{ x^6 + x^5 + x^4 - 28 x^3 + x^2 + x + 1=0}}}...factor

{{{(x^2 - 3 x + 1) (x^4 + 4 x^3 + 12 x^2 + 4 x + 1)=0}}}


if {{{(x^2 - 3 x + 1) =0}}}....use quadratic formula to ind solutions


 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}....{{{a=1}}},{{{b=-3}}},{{{c=1}}}


 {{{x = (-(-3) +- sqrt( (-3)^2-4*1*1 ))/(2*1) }}}


 {{{x = (3 +- sqrt( 9-4 ))/2 }}}

{{{x = (3 +- sqrt( 5 ))/2 }}}

real solutions are:

{{{x[1] = 3/2 + sqrt(5)/2}}}

{{{x[2] = 3/2 - sqrt(5)/2}}}


if {{{x^4 + 4 x^3 + 12 x^2 + 4 x + 1=0}}} you will get only complex solutions; so, disregard it

the sum of the real solutions will be:


{{{x[1]+x[2] = 3/2 + sqrt(5)/2+3/2 - sqrt(5)/2}}}

{{{x[1]+x[2] = 3/2 + cross(sqrt(5)/2)+3/2 - cross(sqrt(5)/2)}}}

{{{x[1]+x[2] = 3/2 +3/2 }}}

{{{x[1]+x[2] = 6/2 }}}

{{{x[1]+x[2] = 3 }}}-> your answer