75 = x^2 + y^2 + z^2

[abehrman]

75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?

Is there a way that this can be done except by trial and error? Are there certain numbers that I should start with?

[nishant_gourav]

7,5,1

[shilpman]

the-number-75-can-be-written-as-the-sum-of-the-squares-t2175.html?hilit=75%20numbers

[debasish.banerjee]

can someone pls. explain how 7,5,1 was chosen?

[kevinmarmstrong]

list the perfect squares less than 75:

1 4 9 16 25 36 49 64

Could the sum involve 64? The sum of the other two squares would have to be 11: impossible.

How about 49? The sum of the other two squares would have to be 26= 25 + 1

Thus 75= 7^2 + 5^2 +1^2

[RonPurewal]

Is there a way that this can be done except by trial and error?

unfortunately... not really.

takeaway:
do not expect a "textbook solution" for every problem.
if a problem has a SMALL NUMBER OF POSSIBILITIES, you can expect to have to try those possibilities, one by one.

Are there certain numbers that I should start with?

see here:
post7260.html#p7260