Question 415100: "i have found two whole numbers whose squares add to 145", Alec claimed
"i bet one is odd and the other is even", said Ann
"how did you know that?" asked Alec
Tell him how ann knew
Ann found two different pars of numbers that met Alec's condition
Can you find two pair,too?
Begin by listing all the square numbers up to 145
PLEASE HELP!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First, let's list all the perfect squares up to 145
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Through trial and error, you'll find that
64 + 81 = 145
and
1 + 144 = 145
Notes: 1^2 = 1, 8^2 = 64, 9^2 = 81, and 12^2 = 144
Since 145 is an odd number, this must mean that one of the numbers is odd while the other is even. Why? Recall that the sum of two even numbers is even and the sum of two odd numbers is also even. For example, 2+6 = 8 (even + even = even) and 1+9 = 10 (odd + odd = even). So the two numbers CANNOT have the same parity (ie be both even or odd at the same time)
So therefore, one number must be odd while the other must be even for the sum to be odd (since odd + even = odd, eg: 1+6 = 7)
If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
|
|
|
