If `(a+b) : sqrt(ab) = 4:1` then find a:b.

If (a+b):sqrt(ab) = 2:1 find a:b.

If (a+b) alpha sqrt(ab) , then show that (sqrta+sqrtb) alpha (sqrta-sqrtb) .

If x = (8ab)/(a+b) , then find the value of ((x+4a)/(x - 4a) + (x+4b)/(x-4b)) .

If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

If a - b = - 1 then find the value of (a^(3)-b^(3)+3ab+1)

If a = (sqrt5 +1)/(sqrt5-1) and b = (sqrt5-1)/(sqrt5+1) then find the value of (5a^(2) -3ab +5b^(2))

If a/2=b/3 =c/4 =(3a-ab+4c)/p , then find the value of p.

If a = (sqrt3+1)/(sqrt3-1) and ab=1 , then find (a^(2) + ab + b^(2))

If a = (sqrt3-1)/(sqrt3+1) and ab=1 , then find (a^3 + b^3)