Three Homogeneous Quadratics

Algebra Level 4

Given positive real values j,k j, k and ll such that j2+k2+jk=9k2+l2+kl=16l2+j2+lj=25, \begin{array}{l l} j^2 +k^2 + jk & = & 9 \\ k^2 + l^2 + kl & = & 16\\ l^2 + j^2 + lj & = & 25,\\ \end{array} (j+k+l)2 (j + k + l)^2 has the form a+bc a + b \sqrt{c} , where a,ba, b and cc are integers and c c is not a multiple of any square number. What is a+b+c a + b + c?

×

Problem Loading...

Note Loading...

Set Loading...