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