Three consecutive integers whose sum and product both equal 0
Answers
Answered by
6
1.1,2, 3
Sum 1+2+3=6
Product =1*2*3 =6
2. -1,0,1
Sum - 1+0+1=0
Product - 1*0*1=0
3. -1,-2,-3
Sum - 1-2-3=-6
Product - 1*-2*-3 = - 6
Only three sets are there.
Let the numbers be a-1,a, a+1
Sum a - 1 +a +a +1 =3a
Product a(a+1)(a-1) =a^3 - a
Since, sum = product
a^3 - a = 3a
a^3 - 4a = 0
It's a cubic equation.
So, there will be at most 3 solutions for a.
i.e a =-2, 0, 2
Thanks.
Sum 1+2+3=6
Product =1*2*3 =6
2. -1,0,1
Sum - 1+0+1=0
Product - 1*0*1=0
3. -1,-2,-3
Sum - 1-2-3=-6
Product - 1*-2*-3 = - 6
Only three sets are there.
Let the numbers be a-1,a, a+1
Sum a - 1 +a +a +1 =3a
Product a(a+1)(a-1) =a^3 - a
Since, sum = product
a^3 - a = 3a
a^3 - 4a = 0
It's a cubic equation.
So, there will be at most 3 solutions for a.
i.e a =-2, 0, 2
Thanks.
Similar questions