Expand (x−1x+5)2\Big(x - \dfrac{1}{x} + 5\Big)^2(x−x1+5)2
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Given,
⇒ (x−1x+5)2\Big(x - \dfrac{1}{x} + 5\Big)^2(x−x1+5)2
Expanding,
⇒(x−1x+5)(x−1x+5)⇒x2−1+5x−1+1x2−5x+5x−5x+25⇒x2+1x2−10x+23+10x.\Rightarrow \Big(x - \dfrac{1}{x} + 5\Big)\Big(x - \dfrac{1}{x} + 5\Big) \\[1em] \Rightarrow x^2 - 1 + 5x - 1 + \dfrac{1}{x^2} - \dfrac{5}{x} + 5x - \dfrac{5}{x} + 25 \\[1em] \Rightarrow x^2 + \dfrac{1}{x^2} - \dfrac{10}{x} + 23 + 10x.⇒(x−x1+5)(x−x1+5)⇒x2−1+5x−1+x21−x5+5x−x5+25⇒x2+x21−x10+23+10x.
Hence, (x−1x+5)2=x2+1x2−10x+23+10x.\Big(x - \dfrac{1}{x} + 5\Big)^2 = x^2 + \dfrac{1}{x^2} - \dfrac{10}{x} + 23 + 10x.(x−x1+5)2=x2+x21−x10+23+10x.
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