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Algebra Level 5

The smallest positive integral value of $a$ for which the greater root of the equation $x^2-(a^2+a+1)x+a(a^2+1)=0$ lies between the roots of the equation $x^2-a^2x-2(a^2-2)=0$ is:

\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}

\sqrt{\dfrac{27}{\sqrt{\dfrac{27}{\sqrt{\dfrac{27}{\sqrt{\cdots}}}}}}}

\sqrt 5\sqrt{\sqrt 5\sqrt{\sqrt 5\sqrt{\sqrt 5\sqrt{\cdots}}}}

\sqrt{4\sqrt{4\sqrt{4\sqrt{\cdots}}}}

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Are you ready for JEE-2?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 8 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.