If `x+1,4x+1," and "8x+1` are in geometric progrssion, then what is the non-trivial value of x ?

Options

A. -1
B. 1
C. `(1)/(8)`
D. `(1)/(4)`

Answer

C

Explanation

If `(x+1),(4x+1)" and "(8x+1)` are in GP.
then `(4x+1)^(2)=(x+1)(8x+1)`
`implies" "16x^(2)+8x+1=8x^(2)+x+8x+1`
`implies" "8x^(2)-x=0impliesx(8x-1)=0`
`implies" "x=0,(1)/(8),[(1)/(8)" is non-trivial value"]`