CDS 2026 (I) Elementary Mathematics, question 83

Topic: Algebra

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Passage · Q83 to Q84

16(x4+1x4)−257=016\left( x^{4}+\frac{1}{x^{4}} \right)-257=0

Q83

What is (x2+1x2)\left( x^{2}+\frac{1}{x^{2}} \right) equal to ?

  1. (a) 2516\frac{25}{16}
  2. (b) 2116\frac{21}{16}
  3. (c) 194\frac{19}{4}
  4. (d) 174\frac{17}{4}Correct answer

Solution.

Answer: (d) 174\frac{17}{4}

  1. The shared equation is 16(x4+1/x4)=25716\left( x^{4} + 1/x^{4} \right) = 257.
  2. Therefore (x2+1/x2)2=x4+2+1/x4=257/16+2=289/16\left( x^{2} + 1/x^{2} \right)^{2} = x^{4} + 2 + 1/x^{4} = 257/16 + 2 = 289/16.
  3. For real nonzero x,x2+1/x2x,x^{2} + 1/x^{2} is positive, so take the positive square root.