The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

Asked by shahishrishti | 27th Jul, 2014, 07:36: PM

Expert Answer:

L e t space a minus d comma space a comma space a plus d space b e space t h e space n u m b e r s space i n space A. P. T h u s comma space a minus d plus a plus a plus d equals 12 rightwards double arrow 3 a equals 12 rightwards double arrow a equals 4 A l s o comma space w e space h a v e comma open parentheses a minus d close parentheses to the power of e plus a cubed plus open parentheses a plus d close parentheses cubed equals 288 rightwards double arrow 3 a cubed plus 24 d squared equals 288 rightwards double arrow 3 cross times 64 plus 24 d squared equals 288 rightwards double arrow 192 plus 24 d squared equals 288 rightwards double arrow 24 d squared equals 288 minus 192 rightwards double arrow 24 d squared equals 96 rightwards double arrow d squared equals 4 rightwards double arrow d equals plus-or-minus 2 T h u s comma space t h e space n u m b e r s space a r e : space 4 minus 2 comma space 4 comma space 4 plus 2 space o r space 4 minus open parentheses minus 2 close parentheses comma 4 comma 4 plus open parentheses minus 2 close parentheses T h a t space i s comma space t h e space n u m b e r s space a r e : space 2 comma 4 comma 6 space o r space 6 comma space 6 comma 4 comma 2

Answered by Vimala Ramamurthy | 28th Jul, 2014, 10:19: AM