If a,b,c are in GP and x,y are the arithmetic means of a,b and b,c respectively,prove that
1)ax + cy = 2.
2)1x + 1y =2b .
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1 Answers
36I think i can kill this...
b/a = c/b = (b + c)/(a + b) = 2y/2x = y/x
now, b/a = y/x and c/b = y/x
=> a/x = b/y and b/x = c/y
=> a/x + c/y = b/y + b/x ---- (i)
Now, a + b = 2x => a/x + b/x = 2 but, a/x = b/y => b/x + b/y = 2
putting, this value in (i) we get,
a/x + c/y = 2
and since, b/x + b/y = 2 => 1/x + 1/y = 2/b
Thus proved...
my teacher told me of this method... and it really works