I have tried for more than hour now to solve this one.
If $4x^2+9y^2+z^2-6xy-3yz-2zx=0$ and an amount of $\rm Rs.3575/$- is distributed among three persons $\rm A,B,C$ in the ratio $\rm x:y:z$. Then the amount which is given to $\rm B$ is
$\rm A) \,\,Rs.600/$- $\qquad\rm B) \,\,Rs.750/$- $\qquad\rm C) \,\,Rs.650/$- $\qquad\rm D) \,\,Rs.700/$-
To solve for three variables (I only need B's amount though), we'll need three equations. However, I see only two in this question - the quadratic equation and then the equation from ratio and the total sum.$(x+y+z=3575)$
I thought that I could use the formula for $(a+b+c)^2$ as the third one, but that doesn't seem to do any good to me. I'm even starting to doubt if something is amiss with the question. I don't need the solution, I want to know the approach.
For the record, this is not homework. Shameful enough, I'm the volunteer teacher preparing a few kids for a competitive test and this question is from last year.