In the equadratic equation `A(sqrt3-sqrt2)x^2+B/(sqrt3+sqrt2) x+C=0` with `alpha, beta` as its roots. If `A=(49+20sqrt6)^(1/4)`; B=sum of the infinite G.P as `8sqrt3+(8sqrt6)/sqrt3+(16)/sqrt3+.....oo and |alpha-beta|=(6sqrt6)^k` where `k=log_6 10-2 log_6 sqrt5+log_6 sqrt((log_6 18 + log_6 72)),` then find the value of C.

In the quadratic equation A(sqrt(3)-sqrt(2))x^(2)+(B)/(sqrt(3)+sqrt(2))x+C=0 with alpha,beta as its roots.If A=(49+20sqrt(6))^((1)/(4));B= sum of the infinit G.P. as 8sqrt(3)+8(sqrt(6))/(sqrt(3))+(16)/(sqrt(3))+........oo and | alpha-beta|=(6sqrt(6))^(k)k=log_(6)sqrt(10)-2log_(6)sqrt(5)+log_(6)sqrt(log_(6)18+log_(6)72) then find the value of C.

(sqrt 3 + sqrt 2)^6 + (sqrt 3 - sqrt 2)^6 =

(3sqrt2+sqrt3-sqrt6)/(2sqrt3-3sqrt2+sqrt6)=

(3-sqrt(6))/(3+2sqrt(6))=a sqrt(6)-b

Evaluate log_2sqrt6+log_2 sqrt(2/3)

Factorize 6+2sqrt(3)-sqrt(8)-2sqrt(6)

Find the value of 4^(5log_(4sqrt2)(3-sqrt6)-6log_8(sqrt3-sqrt2)) .

Find the value of (log sqrt(27) + log sqrt(8) - log sqrt(125))/(log 6 - log 5)

Prove that (log3sqrt(3)+log sqrt(8)-log sqrt(125))/(log6-log5)=(3)/(2)