Question

The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers.

Answer 1

Let the numbers be (a – d), a, (a + d). Then,

Sum = – 3

(a – d) + a + (a + d) = – 3

3a = – 3

a = – 1

Product = 8

(a – d) (a) (a + d) = 8

a ( $a^2$ – $d^2$) = 8

(–1) (1 – $d^2$) = 8

$d^2$ = 9

d = ± 3

If d = 3, the numbers are –4, –1, 2. If d = – 3, the numbers are 2, – 1, –4.

Thus, the numbers are –4, –1, 2, or 2, – 1, – 4.