Algebra

Radical Expressions and Equations

Infinitely Nested Radicals

         

What's the correct statement about xx?

x=xxx x = \sqrt{x - \sqrt{x - \sqrt{x \ldots } }}

Hint: The expression marked in purple below is equivalent to x x . Use substitution!

x=333 x = \sqrt{\sqrt{3\sqrt{\sqrt{3\sqrt{\sqrt{3} \ldots}}}}}

Which of these is a solution for xx?

Hint: The expression marked in purple below is equivalent to x x . Use substitution!

x=252533 x = \sqrt{2\sqrt[3]{5\sqrt{2\sqrt[3]{5 \ldots}}}}

Which of these is a solution for xx?

x=2x32x3 x = \sqrt{2 \sqrt{x \sqrt{3 \sqrt{2 \sqrt{x \sqrt{3 \ldots } }}}}}

What's the nonzero solution for x x ?

x=aaaa x = \sqrt{a \sqrt{a \sqrt{a \sqrt{a \ldots }}}}

If a a is nonzero, which of these does x x equal?

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