Question

The sum of three numbers in an AP is -3 and their product is 8, the common difference of the AP is -------------------

Answer 1

Answer:

common difference=3

Step-by-step explanation:

Let the numbers be x,x+d,x+2d.

x+x+1d+x+2d=(-3)

3x+3d=-3

3(x+d)=-3

x+d= -1

x= -(d+1)

(x)(x+d)(x+2d)=8

-(d+1)(-d-1+d)(-d-1+2d)=8

(d+1)(d-1)=8

(d)²-(1)²=8

(d)²-1=8

(d)²=9

d=√9

d=3

So the common difference of the AP is 3.

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Answer 2

Let the no. is be

a-d, a, a+d.... AP.

Sum of AP is -3

a-d+a+a+d= -3………-d & +d cancel

3a=-3

a=-1

Now

a(a-d) (a+d) =8

a(a²-d²) =8

Now, a=-1 put

1²-d²=8-1

1-d²=7

-d²=7-1

-d²=6

d²=-6

d= √-6

Therefore common difference is √-6