the sum of three numbers in an arithmetic progression is 15 and their product is 105. Find the numbersIt has to do with Arithmetic Progression and the formula

Expert Answers
embizze eNotes educator| Certified Educator

Let x,x+d and x+2d be the three numbers.

Then x+x+d+x+2d=15 or 3x+3d=15 ==>x+d=5

We are also given x(x+d)(x+2d)=105

Substituting `5-x` for d we get:

x(x+5-x)(x+2(5-x))=105

x(5)(-x+5)=105

`-5x^2+50x=105`

`5x^2-50x+105=0`

`5(x-3)(x-7)=0` so x=3 or x=7

If x=7 then d=-2 and we have 7,5,3 as the numbers.

If x=3 then we have 3,5,7 as the numbers.

---------------------------------------------------------------

The sum of 3,5,7 is 15 and the product is 105 so the required numbers are 3,5,7.

---------------------------------------------------------------