Question

Solve the equations: m² + n2 = 29; m + n= 7

Answer 1

We have the following:

$\begin{gathered} m^2+n^2=29 \\ m+n=7;m=7-n \end{gathered}$

replacing:

$\begin{gathered} (7-n)^2+n^2=29 \\ 49-14n+n^2+n^2=29 \\ 2n^2-14n+20=0 \\ n^2-7n+10=0 \\ (n-5)\cdot(n-2)=0 \\ n-5=0=>n=5 \\ n-2=0=>n=2 \end{gathered}$

solving for n:

n = 5

n = 2

replacing:

$\begin{gathered} m=7-5 \\ m=2 \\ m=7-2 \\ m=5 \end{gathered}$

The solution is:

(2, 5) and (5, 2)