MathematicsHard129×since 2002Q5157If α,β\alpha, \betaα,β are the roots of the equation x2−(5+3log35−5log53)x+3(3(log35)13−5(log53)23−1)=0x^{2}-\left(5+3^{\sqrt{\log _{3} 5}}-5^{\sqrt{\log _{5} 3}}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0x2−(5+3log35−5log53)x+3(3(log35)31−5(log53)32−1)=0, then the equation, whose roots are α+1β\alpha+\frac{1}{\beta}α+β1 and β+1α\beta+\frac{1}{\alpha}β+α1, is :A3x2−20x−12=03 x^{2}-20 x-12=03x2−20x−12=0B3x2−10x−4=03 x^{2}-10 x-4=03x2−10x−4=0C3x2−10x+2=03 x^{2}-10 x+2=03x2−10x+2=0D3x2−20x+16=03 x^{2}-20 x+16=03x2−20x+16=0Check answerSkip