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SSC Selection Post 2022 PYQ — Question 70

SSC Selection Post - Higher Secondary Level - 4 Aug 2022 - Shift 3 • Quantitative Aptitude • Q70

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Simplify the following product :

(x+1x)(x−1x)(x2+1x2)( x + \frac{1}{x})( x - \frac{1}{x})( x^2 + \frac{1}{x^2})

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Correct answer: D

Explanation

The correct answer is option 4 i.e.  x4−1x4x^4 - \frac{1}{x^4}

Use identity on first two terms ,(x+1x)(x−1x)=x2−1x2\left(x + \frac{1}{x}\right)\left(x - \frac{1}{x}\right) = x^2 - \frac{1}{x^2}

Now multiply with the third factor,

(x2−1x2)(x2+1x2)\left(x^2 - \frac{1}{x^2}\right)\left(x^2 + \frac{1}{x^2}\right)= x4−1x4x^4 - \frac{1}{x^4}

Use the identity : (a - b)(a + b) = a2−b2a^2 - b^2