If u and v are real numbers and `(u+3)^(2)+(v+5)^(2)=0`, then find the values of u and v.

If x^(2)+y^(2)=4 and u^(2)+v^(2)=9 where x,y,u and v are real numbers then find the maximum value of (xu-yv)

If u and v are the roots of the equation x^2+2x-2=0 , then the value of log_2(u^2+v^2)-log_2u^2-log_2v^2 is 2 (2) -1 (3) 1 (4) 0 (5) -2

If u,v,ware real numbers such that u^(3) - 8v^(3) - 27w^(3) = 18uvw , which one of . the following is correct ?

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2v+3w=6,4u+5v+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2v+3w=6,4u+5v+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to

Let u,v,w be rela numbers in geometric progression such that u gt v gt w. Suppose u ^(40)= v ^(n) = w ^(60). Find the value of n .