Chapter 0, Problem 6P

To determine

To find: the required integers

Answer to Problem 6P

Therefore, the required consecutive numbers are,32 and 34

Explanation of Solution

Given:

The product of two consecutives even integers is 1088.

Calculation:

Use the trial and error method

Look for square of any number which is nearest to and smaller than given number, 1088

The reason for this is if the number is chosen, then its product with consecutive even number (larger one) should give a product more than its square and should be equal to given number. If not, then no such consecutive even numbers are possible.

Now, Start with,

  $\begin{array}{l}{30}^2=900\hfill \\ {40}^2=1600\hfill \end{array}$

Since 1088 is closer to 900 start with 33

  ${33}^2=1089$

It fails our requirement as it is more than 1088

Thus, take 32

And ${32}^2=1024$

And its greater even consecutive number is, 34

Thus, find $32\times 34=1088$

Therefore, the required consecutive numbers are,32 and 34

Conclusion:

Therefore, the required consecutive numbers are,32 and 34