Question

the difference of the square of two numbers is 17 and the difference between the numbers is i. find the numbers

Answer 1

Answer:

The difference between two consecutive squares is an ever increasing odd number.

So, the sequence 1, 4, 9, 16, 25, 36, 49, 64, 81 has difference between consecutive members is 3, 5, 7, 9, 11, 13, 15, 17.

81 - 64 is 17; therefore the number you are looking for is sqrt(81), or 9.

Anther way to get this is:

(n + 1) ^ 2 - n^ 2 = 17

n^2 + 2n + 1 - n^2 = 17

2n + 1 = 17

2n = 16

n = 8

So, if n = 8, then n+1, the larger number, = 9.

Finally, the general solution for problems of this form is: If the difference between two consecutive squares is N, then to get the smaller of the two numbers, subtract 1 from N and divide by 2; to get the larger of the two, add 1 to N and then divide by 2.