Quadratic equation

Algebra Level 4

If aa and bb are the roots of the equation x2+10x7=0 x^{2} + 10x - 7 = 0, find the value of

a12+b127(a10+b10)2(a11+b11).\large \dfrac{ a^{12} + b^{12} - 7( a^{10} + b^{10})}{ 2( a^{11} + b^{11})}.

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