ICSE Class 10 Answered

Let the numbers are  a ,  a r ,  a r² 

Product of three numbers,   a × ( a r ) × ( a r² ) =  (ar)³ = 3375

From above expression, we get ,  (ar )³ =  (15)³ 

hence   ( a r ) = 15  ....................... (1)

Product of first and second number = ( a² r )

Product of second anf third number = ( a² r³ )

we get , ( a² r ) + ( a² r³ )= 750

above expression can be written as ,    (a r ) [ a + a r² ] = 750 ...............(2)

By substituting (a r ) from eqn.91) , above eqn.(2) is simplified as

[ a + a r² ] = 50

a [ 1 + r² ] = 50 ...................... (3)

By dividing eqn.(3) by eqn.(1) , we get

From above expression, we get the following quadratic equation

3 r² - 10 r + 3 = 0

3 r ( r- 3 ) - ( r- 3 )

( 3 r -1 ) ( r - 3 ) = 0

Hence we get r = 3.

By substituting r in eqn.(1) , we get a = 5

Hence the numbers are  5 , 15 and 45