Math  /  Algebra

QuestionFind fixed points of the sequence defined by an+1=12(an+3an)a_{n+1}=\frac{1}{2}\left(a_{n}+\frac{3}{a_{n}}\right).

Studdy Solution
Take the square root of both sides of the equation to solve for aa. Remember that the square root has two solutions, one positive and one negative.
a=3,a=3a = \sqrt{3},\, a = -\sqrt{3} The fixed points of the sequence are 3\sqrt{3} and 3-\sqrt{3}.

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