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

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+3G^3/H x-G^3=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 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, b and c are in G.P and x and y, respectively , be arithmetic means between a,b and b,c then

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

If A, G and H are respectively arithmetic , geometric and harmonic means between a and b both being unequal and positive, then A = (a+b)/2 rArr a + b = 2A , G = sqrtab rArr ab = G^2 and H = (2ab)/(a + b) rArr G^2 = AH . From above discussion we can say that a , b are the roots of the equation x^2 - 2A x + G^2 = 0 Now, quadratic equation x^2 - Px + Q = 0 and quadratic equation a(b-c)x^2 + b(c - a)x + c(a-b) = 0 have a root common and satisfy the relation b = (2ac)/(a+c) , where a, b, c are real numbers. The value of [2P - Q] is (where [.] denotes the greatest integer function)