Question

Simplify: (a+ 1/a)² + ( a- 1/a)²​

Answer 1

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$(a+\frac{1}{a})^{2} +(a-\frac{1}{a} )^{2} \\\\=(a^{2}+\frac{1}{a^{2} } +2\times a \times\frac{1}{a})+(a^{2} +\frac{1}{a^{2} } -2\times a \times \frac{1}{a})\\\\=a^{2}+ a^{2}+\frac{1}{a^{2} }+ \frac{1}{a^{2} } +2-2\\\\=2a^{2} +\frac{2}{a^{2} }\\\\=2(a^{2}+\frac{1}{a^{2} } )$

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