Perfect squares Polynomials

Algebra Level 3

\[ lx^2+mx+n \\ mx^2+nx+l \\ nx^2+lx+m \]

For distinct non-zero values of \(l,m\) and \(n\). It is given that all of the algebraic expressios above are perfect square polynomials, find the value of \( \dfrac{l +m}n \).

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