Well, can you write an expression for each term in terms of an algebraic variable? For example, call the first term , the second term , and so on. Then simplify the equation to a tautology (something which is obviously true) such as .
Hey!
I am trying to solve this problem...
2^2+3^2+6^2=7^2
and
3^2+4^2+12^2=13^2
(^2 represents squared)
I have found out that the first two numbers need to be consecutive. The third number is the product of the first two and the 'answer' is the sum of the third number plus 1. This works for all numbers but i am not sure why!?!?!?
Any suggestions?
What problem are you trying to solve? Certainly NOT that
"2^2+3^2+6^2=7^2" and "3^2+4^2+12^2=13^2" because those are trivial arithmetic: 4+ 9+ 35= 13+ 36= 49 and 9+ 16+ 144= 25+ 144= 169.
Are you trying to find some general patterns so that a sum of three squares is equal to a square?
Thank you for your message hallsofivy!
I have established that:-
The first two numbers in the equation are consecutive (eg and )
The third number is the product of the first two (eg
The 'answer' is one more that the third number (eg
What i want to know is why is this the case? What is special about using these rules and numbers that makes the rules work.
Good. Now “do” the RHS of the equation (what is one more the than the third number, quantity squared?) and manipulate the resulting equation until you arrive at a tautology (FYI upon working out your example, I arrived at , although there are many other ways). As long as the steps you used are reversible, you have an answer as to why this is pattern holds for arbitrary numbers.