Question 1128329
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The equation

    2x^2 - 2kx + 4 = 0 

is equivalent to  (after dividing both sides by 2)


    x^2 - kx + 2 = 0.      (1)


We are given that  {{{sqrt(3)-1}}}  is the root of the original equation; hence, the equation (1) with the leading coefficient 1 has this root, too.


Then, applying the Vieta's theorem, the other root of the equation (1) is


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


Thus we know BOTH ROOTS of the equation (1) (even without solving it explicitly (!) ). They are


    {{{sqrt(3)-1}}}  and  {{{sqrt(3)+1}}}.


Again, according to Vieta's theorem, the sum of these roots is the coefficient at x in equation (1) taken with the opposite sign:


    k = {{{sqrt(3)-1}}} + {{{sqrt(3)+1}}} = {{{2*sqrt(3)}}}.


<U>Answer</U>.  k = {{{2*sqrt(3)}}}.
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Solved.  &nbsp;&nbsp;// &nbsp;&nbsp;Option C).