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SSC Selection Post 2022 PYQ — Question 67

SSC Selection Post - Graduation Level 2022 - 10 Feb 2022 - Shift 3 • Quantitative Aptitude • Q67

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If x - 1x1\over{x}= 2\sqrt2, then what is the value of x4−1x2x2−1x^4-{1\over{x^2}}\over{x^2}-1?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 5.

x - 1/x = √2

⇒ x2 + 1/x2 = (√2)2 + 2 = 4

Now, x4−1x2x2−1{x^4-{1\over{x^2}}\over{x^2}-1}

=x6−1x2x2−1=\frac{\frac{x^6-1}{x^2}}{x^2-1}

=x6−1x2(x2−1)=\frac{x^6-1}{x^2(x^2-1)}

=x4+x2+1x2=\frac{x^4+x^2+1}{x^2}

= x2 + 1 + 1/x2

= 4 + 1 = 5