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# Expand the expression: $(x + \large\frac{1}{x}$$)^6 \begin{array}{1 1}x^6 + 6x^4 + 15x^2 + 20 + 15\large\frac{1}{x^2} + 6\large\frac{1}{x^4} + \large\frac{1}{x^6} \\ x^6 + 6x^4 + 15x^2 + 15\large\frac{1}{x^2} + 6\large\frac{1}{x^4} + \large\frac{1}{x^6} \\ x^6 + 5x^4 + 20x^2 + 25 + 5\large\frac{1}{x^2} + 20\large\frac{1}{x^4} + \large\frac{1}{x^6} \\ x^6 + 15x^4 + 6x^2 + 20 + 6\large\frac{1}{x^2} + 15\large\frac{1}{x^4} + \large\frac{1}{x^6}\end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • (a+b)^n = \large \sum \limits_{k=0}^{n}\;$$^n \large C$$_k \; a^{n-k}b^k =\; ^n \large C$$_0\;a^nb^0 +\; ^n \large C$$_1\;a^{n-1}b^1+.... ^n\large C$$_n\;a^0b^n$, where $b^0 = 1 = a^{n-n}$
Given $(x + \large\frac{1}{x}$$)^6 \rightarrow a = x and b = \large\frac{1}{x} \Rightarrow (x + \large\frac{1}{x}$$)^6 = \large \sum \limits_{k=0}^{6}\; $$^6 \large C$$_k \; x^{6-k}(1/x)^k$

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