I`ve seen the answer to this problem before but I don`t see how is it formulated, could someone please explain?

"Find all triples (a, b, c) such that all three of the following equations are satisfied:

a(b + c - 5) = 7

b(a + c - 5) = 7

a² + b² = 50.

Guest Nov 2, 2022

#2**0 **

\(a(b+c-5)=7 \rightarrow ab+ac-5a=7 \dots(1) \\ b(a+c-5)=7 \rightarrow ab+bc-5b =7 \dots (2)\\ (1) - (2) \rightarrow ac-bc-5a+5b=0,\\ c(a-b)-5(a-b)=0,\\ (a-b)(c-5) =0,\\ a=b, \text{ or }c=5.\)

Now check the consequences of each one. There are multiple solutions.

Ignore the local idiot responsible for #1.

Guest Nov 3, 2022