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`.

If A and G are respectively arithmetic and geemetric mean between positive no.a and b; then A>G

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 x^(3)-3Ax^(2)+3(G^(3))/(H)x-G^(3)=0

Let A;G;H be the arithmetic; geometric and harmonic means of two positive no.a and b then A>=G>=H

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