Let a,x,b be in A.P, a,y,b be in G.P and...

Let `a,x,b` be in `A.P`, `a,y,b` be in `G.P` and `a,z,b` be in `H.P`. If `x=y+2` and `a=5z`, then

`y^(2)=xz`

`x gt y gt z`

`a=9`, `b=1`

`a=1//4`, `b=9//4`

Text Solution

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The correct Answer is:

A, B, C

`(a,b,c)` `2x=a+b`
`y^(2)=ab`
`z=(2ab)/(a+b)`
`x=y+2`
and `a=5z`
`z=(2y^(2))/(2x)`
`impliesy^(2)=xz`
`x=y+2`
`:.(a+b)/(2)=sqrt(ab)+2`………`(i)`
and `a=5((2ab))/(a+b)`
`implies(a+b)=10b`
`impliesa=9b`
`:.` from `(i) (9b+b)/(2)=sqrt(9b^(2))+2`
`implies5b=3b+2`
`impliesb=1`
So `a=9`
`implies x gt y gt z`

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If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that x=9z and agt0,bgt0 , then

`|y|=3zandx=3|y|`

`y=3|z|and|x|=3y`

2y=x+z

none of these

Let a, x, b in A.P, a, y, b in GP a, z, b in HP where a and b are disnict positive real numbers. If x = y + 2 and a = 5z , then which of the following is/are COR RECT ?

`y^(2) = zx`

`x gt y gt z`

`a = 9 , b = 1`

`a = (1)/(4), b = -(9)/(4)`

If x,1,z are in A.P. and x,2,z are in G.P., then x,4,z are in

G.P

H.P.