If a - 3-2-2- find the value of a2-1-a2-

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Algebraic Identities

If a = 3+2√2,...

Question

If a = 3+2 $\sqrt{2}$ , find the value of $a^{2} + \frac{1}{a^{2}}$ .

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Solution

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a = \frac{3 + \sqrt{5}}{2}

a^{2} + \frac{1}{a^{2}}

a = 3 + 2 \sqrt{2}

\frac{a^{2} + 1}{a^{2}}

a = 2 + \sqrt{3}

a^{2} + \frac{1}{a^{2}}

a = \frac{3 + \sqrt{5}}{2}

a^{2} + \frac{1}{a^{2}}

a = \frac{3 + \sqrt{5}}{2}

a^{2} + \frac{1}{a^{2}}

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