CBSE Class 11-science Answered
The sum of two numbers is 6 times their geometric mean. Show that the numbers are in the ratio 3 + 2?2 : 3 - 2?2 .
Asked by Vikrant | 29 May, 2012, 06:13: PM
Expert Answer
let the two numbers be a,b
then a+b=6[(ab)^1/2].....
next a+b/2[(ab)^1/2]=3
now apply componendo and dividendo......
a+b+2[(ab)^1/2] / a+b-2[(ab)^1/2]=3+1/3-1
(roota+rootb) / (roota-rootb)=root2
now again applying componendo and dividendo...
roota / rootb=root2+1/ root2-1
now squaring both sides....
a / b=3+2root2 / 3-2root2
Answered by | 30 May, 2012, 08:38: AM
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