CBSE Class 11-science Answered
if the sum of two no.s is equal to b times there geometric means show that the show that the no. are in the ratio 3+2root2 :3_2root2
Asked by Apoorva Tiwari | 30 Oct, 2013, 05:36: PM
Expert Answer
Let the two numbers be a and b.
Then ,
a+b = 6 x root ab
a+b = 3 x 2 root ab
a+b / 2 rootab = 3
By componendo and dividendo,
a+b+2 rootab/ a+b - 2root ab = 3+1/3-1
(root a+root b)2 / (root a - root b)2 = 2
root a+ root b / root a - root b = root 2
root a+ root b = root 2 x root a - root2 x root b
root b (1+root2) = root a (root2 - 1)
(1+ root2) / (root2 -1) = root a / root b
(root 2+1)2 / (root2 -1)2 = (root a)2 / (root b)2
3+ 2root 2 / 3- root2 = a/b
Then ,
a+b = 6 x root ab
a+b = 3 x 2 root ab
a+b / 2 rootab = 3
By componendo and dividendo,
a+b+2 rootab/ a+b - 2root ab = 3+1/3-1
(root a+root b)2 / (root a - root b)2 = 2
root a+ root b / root a - root b = root 2
root a+ root b = root 2 x root a - root2 x root b
root b (1+root2) = root a (root2 - 1)
(1+ root2) / (root2 -1) = root a / root b
(root 2+1)2 / (root2 -1)2 = (root a)2 / (root b)2
3+ 2root 2 / 3- root2 = a/b
Answered by | 30 Oct, 2013, 11:15: PM
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