Algebraic Expressions

We need to find the value of . First, rewrite the given equation as: The denominator on the left-hand side can be factored as: Now, equate the two fractions: Now, equate the numerators: Expanding both sides: By comparing the coefficients of and the constant term, we get the system of equations: 1. 2.
Solving this system, we first multiply the first equation by 5: Now subtract the second equation from this: Substitute this into the first equation: Now, substitute into : Thus, and , so:

Step 1: Using the identity for sum of reciprocals of squares
We use the identity: Step 2: Finding required symmetric sums
From Vieta’s formulas applied to the polynomial equation: we obtain the sums: Using the square identity: Thus: Step 3: Conclusion
Hence, the final answer is: