Let a, b, c, d be real numbers in G.P. ...

Let `a, b, c, d` be real numbers in `G.P.` If `u, v, w` satisfy the system of equations `u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4` then show that the roots of the equation `(1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0` and 20x^2+10(a-d)^2 x-9=0` are reciprocals of each other.

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Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2v +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+1/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+(u+v+w)=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2v +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+1/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and '20x^2 +10(a-d)^2 x-9=0 are reciprocals of each other.

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2v+3w=6,4u+5v+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2y+3w=6,4u+5y+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to

If u : v : w = 3 : 6 : 8, then what will be the ratio of (u/v) : (v/w) : (w/u)?

If s:u:v:w=2:9:6:7ands+u+v+w=864 , then what is the value of s+u+w ?

Let `a, b, c, d` be real numbers in `G.P.` If `u, v, w` satisfy the system of equations `u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4` then show that the roots of the equation `(1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0` and 20x^2+10(a-d)^2 x-9=0` are reciprocals of each other.

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