Question

Find all real number x , y , z such that :
(x+y)(y+z)=35 , (y+z)(z+x)=40 and (z+x)(x+y)=56.

Answer 1

For simplification, let \(a=x+y, b=y+z \text{ and } c=z+x\), then
\(ab=35\), \(bc=40\) and \(ca=56\). We can write the following equations:
\(\large \frac{ab}{7}=5 \text{ and } \frac{bc}{8}=5\),
\(\large \frac{bc}{5}=7 \text{ and } \frac{ca}{7}=8\). This might help!

Answer 2

The lat line should be \(\large \frac{bc}{5}=8 \text{ and } \frac{ca}{7}=8.\)