Question

find ten rational number between 2 and 5

Answer 1

tjis is the answe of ur question

Answer 2

Let
$y = 5 \\ x = 2 \\ n = 10 \\ d = \frac{y - x}{n + 1} = \frac{5 - 2}{10 + 1} = \frac{3}{11}$
So, 10 rational numbers between 2&5 are:-
(x+d),(x+2d),(x+3d),(x+4d),(x+5d),(x+6d),(x+7d),(x+8d),(x+9d),(x+10d).
$= (2 + \frac{3}{11} )(2 + 2 \times \frac{3}{11} )(2 + 3 \times \frac{3}{11} ) \\ (2 + 4 \times \frac{3}{11})(2 + 5 \times \frac{3}{11} )(2 + 6 \times \frac{3}{11} ) \\ (2 + 7 \times \frac{3}{11} )(2 + 8 \times \frac{3}{11} )(2 + 9 \times \frac{3}{11} ) \\ (2 + 10 \times \frac{3}{11} ) \\ = ( \frac{22 + 3}{11} )( \frac{22 + 6}{11})( \frac{22 + 9}{11} )( \frac{22 + 12}{11} ) \\ ( \frac{22 + 15}{11} )( \frac{22 + 18}{11} )( \frac{22 + 21}{11} )( \frac{22 + 24}{11} ) \\ ( \frac{22 + 27}{11} )( \frac{22 + 30}{11} ) \\ = ( \frac{25}{11} )( \frac{28}{11} )( \frac{31}{11} )( \frac{34}{11} )( \frac{37}{11} )( \frac{40}{11} ) \\ ( \frac{41}{11} )( \frac{46}{11} )( \frac{49}{11} )( \frac{52}{11})$