Question

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

Answer 1

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)`