Double maxed out

Algebra Level 5

For a positive real number rr, let M(r)M(r) be the largest possible value of F(x,y,z)=x2+yz3 F(x,y,z) = x^2 +yz^3 over all ordered triples of non-negative real numbers (x,y,z),(x,y,z), such that x2+y2+z2=r.x^2+y^2+z^2=\sqrt{r}.

There is a value of r,r, denoted by r r^*, such that F(x,y,z)=M(r)F(x,y,z)=M(r^*) for two different triples (x,y,z)(x,y,z) which satisfy x2+y2+z2=r.x^2+y^2+z^2=\sqrt{r^*}. If r=ab r^* = \frac{a}{b} where aa and bb are coprime positive integers, what is a+ba + b ?

×

Problem Loading...

Note Loading...

Set Loading...