Question

The product of two consecutive odd integers is 63. If x is the smallest of the integers, write an equation in terms of x that describes the situation, and then find all such pairs of integers.
The equation that describes the situation is __________________
The positive set of integers is _________________
The negative set of integers is _________________

Answer 1

9514 1404 393

Answer:

• x(x+2) = 63
• 7, 9
• -9, -7

Step-by-step explanation:

If x is an odd integer, the next greater odd integer is x+2. The product is said to be 63, so the equation is ...

  x(x +2) = 63

__

The equation can be rewritten as ...

  (x +1)² = 64

  x = -1 ±√64 = -1 ±8

The positive solution is x=7, so the positive set of integers is {7, 9}.

The negative solution is x=-9, so the negative set of integers is {-9, -7}.