Question

The product of two positive consecutive integers is 462. Find the integers.

Answer 1

Not possible. The product must be a whole number and odd. For example, 4+5 is 9

Answer 2

21,22

Explanation:

n(n+1)=462

Distribute n through the term in the parentheses.

n2+n=462

Subtract 462 from each side.

n2+n−462=462−462

Write the relationship as a quadratic equation.

n2+n−462=0

Factor the equation.

(n+22)(n−21)=0

Solve.

n+22=0 and n−21=0n=−22 or 21