Question

Prove that the product of the second and third numbers out of four consecutive whole numbers is two greater than the product of the first and the fourth numbers.

Answer 1

Let the four consecutive numbers be x,x+1,x+2,x+3.

Now the product of second and third number=(x+1)(x+2)=x²+3x+2=k

Product of first and fourth number=x(x+3)=x²+3x=k-2

A.T.Q

product of second and third number= product of first and fourth number+2

Hence proved