If A and G are respectively arithmetic and geometric mean between positive no. a and b ; then the quadratic equation having a,b as its roots is `x^2-2Ax+G^2=0`.

Let A;G;H be the arithmetic; geometric and harmonic means between three given no. a;b;c then the equation having a;b;c as its root is

If a, b and c are in G.P and x and y, respectively , be arithmetic means between a,b and b,c then

If A, g and H are respectively arithmetic , geometric and harmomic means between a and b both being unequal and positive, then A = (a + b)/(2) rArr a + b = 2A G = sqrt(ab) rArr G^(2) = ab H = (2ab)/(a+ b ) rArr G^(2) = AH On the basis of above information answer the following questions . If the geometric mean and harmonic means of two number are 16 and 12(4)/(5) , then the ratio of one number to the other is

If A, g and H are respectively arithmetic , geometric and harmomic means between a and b both being unequal and positive, then A = (a + b)/(2) rArr a + b = 2A G = sqrt(ab) rArr G^(2) = ab H = (2ab)/(a+ b ) rArr G^(2) = AH On the basis of above information answer the following questions . The sum of AM and GM of two positive numbers equal to the difference between the numbers . the numbers are in the ratio .

If A, g and H are respectively arithmetic , geometric and harmomic means between a and b both being unequal and positive, then A = (a + b)/(2) rArr a + b = 2A G = sqrt(ab) rArr G^(2) = ab H = (2ab)/(a+ b ) rArr G^(2) = AH On the basis of above information answer the following questions . The numbers whose A.M. and G.M. are A and G is

If g_(1) , g_(2) , g_(3) are three geometric means between two positive numbers a and b , then g_(1) g_(3) is equal to

If A, G and H are the arithmetic mean, geometric mean and harmonic mean between unequal positive integers. Then, the equation Ax^2 -|G|x- H=0 has (a) both roots are fractions (b) atleast one root which is negative fraction (c) exactly one positive root (d) atleast one root which is an integer

If A and G are the arithmetic and geometric means respectively of two numbers then prove that the numbers are (A+sqrt(A^(2)-G^(2)))and(A-sqrt(A^(2)-G^(2)))

If x_(1) and x_(2) are the arithmetic and harmonic means of the roots fo the equation ax^(2)+bx+c=0 , the quadratic equation whose roots are x_(1) and x_(2) is

If a be one A.M and G_1 and G_2 be then geometric means between b and c then G_1^3+G_2^3=