If `log_(2n)1944=log_n486sqrt(2)`,then `n^6=2^alpha.3^beta`, then `alpha+beta` is equal to?

If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0, then the value of alpha ^(2) + alpha beta is equal to :

If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0, then the value of alpha ^(2) + alpha beta +beta^2 is equal to :

If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0, then the value of alpha ^(2) + alpha beta +beta^2 is equal to :

If alpha, beta ar the roots of the quadratic equation x ^(2) -(3+ 2 ^(sqrt(log _(2)3))-3 ^(sqrt(log _(3)2)))x-2 (3 ^(log _(3)2)-2^(log _(z)3))=0, then the value of alpha ^(2) + alpha beta +beta^2 is equal to :

If alpha and beta are the roots of the equation (log_(2)x)^(2)+4(log_(2)x)-1=0 then the value of log_(beta)alpha+log_(alpha)beta equal to

If alpha,beta are the roots of the quadratic equation x^(2)-(3+2^(sqrt(log_(2)3))-3^(sqrt(log_(3)2)))x-2(3^(log_(3)2-2^(log_(2)3)))=0 then the value of alpha^(2)+alpha beta+beta^(2) is equal to

If the solution of the equation log_(x)(125x)*log_(25)^(2)x=1are alpha and beta(alpha

If alpha and beta are the roots of x^(2)-2x +4=0 then alpha^(n) + beta^(n) is equal to

If alpha and beta are solutions of the equation 4log_(3)^(2)x-4log_(3)x^(2)+1=0 then the value of |(sqrt(alpha beta)+1)/(sqrt(alpha beta)-1)| is