Given:
• Sum of three numbers in an AP is -3
• Their product is 24.
To find :
• The numbers .
Solution:
Let the numbers be .
• (a-d) , a , (a+d) .
A/Q ,
• Sum of numbers = -3
=> a-d + a + a+d = -3
=> 3a= -3
=> a = -1 .
Now ,
• Product of numbers = 24
=>( a-d)(a)(a+d)= 24
=> (a²- d²) (a) = 24
=> (1- d²)(-1)=24
=> -1+d²= 24
=> d²= 25
=> d = ±5.
If d = 5 the numbers are :
• a+d , a , a-d = 4 , -1 , -6
If d = -5 the numbers are :
• a+d , a , a -d = -6, -1 , 4 .
The numbers are :
4 , -1 , -6 and -6, -1,4
I hope it will help you.
Regards.