the sum of three numbers of an ap is 27 and their product is 405. find the numbers
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27
Heya User,
--> Let the no.s be ummm, [ a + d ], [ a ] , [ a - d ]
--> Sum = [ a - d ] + [ a ] + [ a + d ] = 27
--> Sum = 3a = 27
=> Mid - Term -> a = 27 / 3 = 9
However,
--> [ a - d ] [ a ] [ a + d ] = 405
=> [ 9 + d ] [ 9 - d ] = 405 / 9 = 45
=> [ 9² - d² ] = 45
=> 81 - 45 = d²
=> d = √36 = ± 6
Either way, the three numbers would be :->
---> [ 9 - 6 ] , 9 , [ 9 + 6 ]
= [ 3 ] , [ 9 ] , [ 15 ] || or || [ 15 ] , [ 9 ] , [ 3 ]
^_^ Just consider [ ] <--- as normal brackets :p
--> Let the no.s be ummm, [ a + d ], [ a ] , [ a - d ]
--> Sum = [ a - d ] + [ a ] + [ a + d ] = 27
--> Sum = 3a = 27
=> Mid - Term -> a = 27 / 3 = 9
However,
--> [ a - d ] [ a ] [ a + d ] = 405
=> [ 9 + d ] [ 9 - d ] = 405 / 9 = 45
=> [ 9² - d² ] = 45
=> 81 - 45 = d²
=> d = √36 = ± 6
Either way, the three numbers would be :->
---> [ 9 - 6 ] , 9 , [ 9 + 6 ]
= [ 3 ] , [ 9 ] , [ 15 ] || or || [ 15 ] , [ 9 ] , [ 3 ]
^_^ Just consider [ ] <--- as normal brackets :p
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15
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