Question

Find three numbers in arithmetic progression whose sum is 9 and product is -165

Answer 1

Answer:

Step-by-step explanation:

I hope the question is

Find three consecutive numbers in arithmetic progression whose sum is 9 and product is -165

let x be the middle number and d be the common difference

then the numbers are x-d, x and x+d

given their sum = 9

sum of three consecutive terms in an ap is same as three times the middle number.

so 3x=9

⇒ x=3

their product = -165

⇒(x-d)x(x+d)= -165

⇒x(x²-d²)= -165

⇒3(9-d²)= -165

⇒3d²=27+165=192

⇒d²=64

⇒d=±8

so the numbers are 3-8, 3, 3+8 or 3-(-8), 3, 3+(-8)

the numbers are -5, 3, 11