Question

1/x+1 , 1/x+2 , 1/x+3 form an Ap find value of x

Answer 1

[1/ ( x + 2 )] - [1 / ( x + 1 )] = [ 1 / ( x + 3 )] - [1 / ( x + 2 )]

If the given terms form an A. P., then the difference of their consecutive terms will be equal.

So , [ ( x + 1 ) - ( x + 2 )] / [ ( x+ 2) ( x +1 )] = [ ( x +2) - ( x + 3 )] / [ ( x+ 3) ( x +2 )]

( x +1 - x - 2 ) / ( x^2 + 3x + 2 ) = ( x + 2 - x - 3 ) / ( x^2 + 5x + 6 )

=> ( - 1 ) ( x^2 + 5x + 6 ) = ( - 1 ) ( x^2 + 3x +2 )

=> x^2 + 5x + 6 - x^2 - 3x - 2 = 0

=> 2x + 4 = 0

=> 2x = 4

=> x = 4/2

=>$<h3>x = 2$

Answer 2

Step-by-step explanation:

x=2................