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

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

In /_\ABC , if (c + a + b) (a + b - c) = ab, find the-value of angleC .

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

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

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

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

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

If the point (a,b), (a',b') and (a-a',b-b') are collinear, then prove that ab' = a'b.