Q82 of 134 Page 4


Find two consecutive odd natural numbers, the sum of whose squares is 202.


Let the two consecutive odd natural numbers be x and x + 2.
x 2 + (x + 2) 2 = 202
x 2 + x 2 + 4x + 4 = 202
2x 2 + 4x + 198 = 0
x 2 + 2x + 99 = 0
x 2 + 11x – 9x + 99 = 0
x(x + 11) – 9(x + 11) = 0
(x – 9)(x + 11) = 0
x – 9 = 0 or x + 11 = 0
x = 9 or x = -11
Therefore the two consecutive odd natural numbers are 9 and 11.

Checking:
9 2 + 11 2 = 81 + 121 = 202.

More from this chapter

All 134 →
80
The product of Ramu's age (in years) five years ago and his age(in years)nine years later is 15. Determine Ramu's present age.
 81

A two-digit number is such that the product of its digits is 12. When 36is added to this number, the digits interchange their places. Find thenumber.

83
Determine two consecutive even positive integers,  the sum of whosesquares is 100.
 84
The sum of two natural numbers is 8. Determine the numbers, if the sum of theirreciprocals ishttps://gs-post-images.s3.amazonaws.com/user_files/63094/15042/images/extra-4_files/Image1295.gif .