- #1
anemone
Gold Member
MHB
POTW Director
- 3,883
- 115
The rational numbers $a,\,b,\,c$ (for which $a+bc$, $b+ac$ and $a+b$ are all non-zero) satisfy the equality $\dfrac{1}{a+bc} =\dfrac{1}{a+b}-\dfrac{1}{b+ac}$.
Prove that $\sqrt{(c−3)(c+1)}$ is rational.
Prove that $\sqrt{(c−3)(c+1)}$ is rational.