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Given that x+y+z=15 when a ,x ,y ,z ,b a...

Given that `x+y+z=15 when a ,x ,y ,z ,b` are in A.P. and `1/x+1/y+1/z=5/3w h e na ,x ,y ,z ,b` are in H.P. Then
(i) G.M. of `a and b` is 3
(ii) One possible value of `a+2b` is 11
(iii) A.M. of `a and b` is 6
(iv) Greatest value of `a-b` is 8

Text Solution

Verified by Experts

Given x + y + z = 15
when a, x, y, z, b are in A.P.
`therefore ` Sum of A.M.S's =` x + y + z = (a+b)/(2) xx3`
`rArr (a+b)/(2) xx3 = 15`
`rArr a + b = 10`
When `(1)/(a),(1)/(x),(1)/(y),(1)/(z).(1)/(b)` are in A.P.
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