What is the positive value of x if x, 6, x-5 are terms of a geometric progression?

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Posted on

`Let`

`x , 6 , x-5`  are in geometric progression.So by def of geometric progresson

`6/x=(x-5)/6`

cross multiply

`6xx6=x xx(x-5)`

`36=x^2-5x`

`x^2-5x-36=0`

`x^2-9x+4x-36=0`

`x(x-9)+4(x-9)=0`

`(x-9)(x+4)=0`

`either`

`x-9=0 `

`or`

`x+4=0`

`x=-4,9`

Since  x is positive therefore   x=9

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