A Square Number

Algebra Level 3

Given real numbers $a,b,c$ satisfying the expression below:.

$\frac{a^{2}}{a^{2}+b^{2}}+\frac{c^{2}}{a^{2}+c^{2}}=\frac{2c}{b+c}$

Can the product $bc$ be written as a square of a real number?

Yes, always. No, never. Sometimes. Paradox

1 solution

Chris Lewis
Jun 26, 2019

Rearranging the given equation, we find $(b-c)(a^2-bc)=0$ , so either $b=c$ , in which case $bc=b^2$ , or $bc=a^2$ . In both cases $bc$ is the square of a real number.

A Square Number

1 solution

1 pending report

Vote up reports you agree with