Quadratic equation

Algebra Level 4

If \(a\) and \(b\) are the roots of the equation \( x^{2} + 10x - 7 = 0\), find the value of

\[\large \dfrac{ a^{12} + b^{12} - 7( a^{10} + b^{10})}{ 2( a^{11} + b^{11})}. \]

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