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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