can u express?

Question

can u express two sum of two squares as sum of other two squares like
9 ^ (2) + 401 ^ (2) =41 ^ (2) + 399 ^ (2)

Answer 1

a^2 + b^2 = c^2 + d^2
a^2 - c^2 = d^2 - b^2
(a-c)(a+c)=(d-b)(d+b)

Choose a value for these products, k. You must be careful how you choose your value of k. k must have two distinct factorizations (m,n) and (p,q) with m,n,p,q all even or all odd.
For example, choose k = 24
24 = 12*2=6*4
a+c = 12, a-c = 2
d+b = 6, d+b = 4
then we get a = 7, c = 5
d = 5, b = 5
so 7^2 + 1^2 = 5^2 + 5^2.

Answer 2

no, it is because when you multiply, is it not equal. 9^(2)+401^(2) is equal to 13,024,881 whereas 41^(2)+399^(2) is equal to 267,616,881. is it like if you are saying two apples is equal to pears, they are two things totally different.

one example where you might say something like this is when both of them correspond
for e.g : 6^(2)+2^(2)= 4^(2)+3^(2)
it is because the sum of one side is really equal to the sum of the other side. do you understand now?

Answer 3

Your question doesn't make sense:

yes, it's possible as long as equation on the left-hand side = the equation on the right-hand side (known as the balanced equation).

Your equation isn't balanced.