Let $x,\,y,\,z>0$ and $a,\,b,\,c$ be real numbers such that $x^2+a^2=y^2+b^2=z^2+c^2=1$.
Prove that $(a+b+c)^2+(x+y+z)^2\ge 1$.
Let $x,\,y,\,z>0$ and $a,\,b,\,c$ be real numbers such that $x^2+a^2=y^2+b^2=z^2+c^2=1$.
Prove that $(a+b+c)^2+(x+y+z)^2\ge 1$.
Last edited by Albert; January 4th, 2017 at 23:31.
Last edited by anemone; January 5th, 2017 at 09:09. Reason: Hide Solution In SP Tags