MathematicsMedium129×since 2002Q5168Let α,β;α>β\alpha, \beta ; \alpha>\betaα,β;α>β, be the roots of the equation x2−2x−3=0x^2-\sqrt{2} x-\sqrt{3}=0x2−2x−3=0. Let Pn=αn−βn,n∈N\mathrm{P}_n=\alpha^n-\beta^n, n \in \mathrm{N}Pn=αn−βn,n∈N. Then (113−102)P10+(112+10)P11−11P12(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}(113−102)P10+(112+10)P11−11P12 is equal toA103P910 \sqrt{3} \mathrm{P}_9103P9B113P911 \sqrt{3} \mathrm{P}_9113P9C112P911 \sqrt{2} \mathrm{P}_9112P9D102P910 \sqrt{2} \mathrm{P}_9102P9Check answerSkip