Question

The sum of 3 number in A.P is -24 and the product is 288.find the number

Answer 1

let the three no in AP are. a-d,. a,. a+d
sum= -24
a-d+a+a+d= -24
3a= -24
a = -8


product= 288
(a-d)a(a+d)=288
(-8)(-8-d)(-8+d)=288
${( - 8)}^{2} - {d}^{2} = \frac{288}{ - 8} \\ 64- {d}^{2} = - 36 \\ {d}^{2} = 64 \times 36 = 100 \\ d = 10$
numbers are -18 , -8, 2