Question

√x+3,√x+5, √x+7 are in AP or not

Answer 1

yes..

$d = \sqrt{x} + 3 - ( \sqrt{x} + 5 ) \sqrt{x} \\ = \sqrt{x} + 3 - \sqrt{x} - 5 \\ = - 2 \\ d = \sqrt{x} + 5 - ( \sqrt{x} + 7) \\ = \sqrt{x} + 5 - \sqrt{x} - 7 \\ = - 2 \\ therefore \: they \: are \: in \: ap$