What is the three numbers in an arithmetic progression whose sum is 6 and product is -64?

1 Answer
Sahar Mulla ❤
Feb 4, 2018

Lets consider the 3 numbers in AP to be, #x-d, x, x+d#, where #d# is the common difference.

So, according to the question, their sum is 6
#=> (x-d) +(x) +(x+d)=6#
#=>3x=6#
#=>x=2#

and their product is -64;
#=>(x-d)(x)(x+d)=-64#
#x(x^2-d^2) = -64#
#2(4-d^2)=-64#
#4-d^2=-32#
#d^2=4+32#
#d=sqrt36#
#d=6#

So, the three numbers are, #x-d, x, x+d#
#=>(2-6), (2), (2+6)#
#=>-4, 2,8#

#color(purple)(-Sahar)#

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