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

Options

A. G.M of a and b is 3
B. one possible value of a + 2b is 11
C. A.M of a and b is 6
D. greatest value of a-b is 8

Answer

A, B, D

Explanation

`x+y+z=3((a+b)/2)`
`rArr15-3((a+b))/2`
`rArra+b=10`
`1/x+1/y+1/z=(3(1/a+1/b))/2`
`rArr5/3=(3(a+b))/(2ab)=(3xx10)/(2ab)`
`rArrab=9` (2)
From (1) and (2), a=9,b=1 or a=1 and b=9. Hence, G.M.
`=sqrt(ab)=3,a+2b=11` or 19.