CDS 2026 (I) Elementary Mathematics, question 86

Topic: Algebra

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Passage · Q85 to Q86

Let x=6+56−5x=\frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}-\sqrt{5}} and y=6−56+5y=\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}+\sqrt{5}}

Q86

What is (x2−xy+y2)\left( x^{2}-xy+y^{2} \right) equal to ?

  1. (a) 487487
  2. (b) 483483
  3. (c) 481481Correct answer
  4. (d) 480480

Solution.

Answer: (c) 481481

  1. The reciprocal definitions give xy=1xy = 1, while rationalising gives x+y=22x + y = 22.
  2. Therefore x2−xy+y2=(x+y)2−3xy=222−3=481x^{2} - xy + y^{2} = (x + y)^{2} - 3xy = 22^{2} - 3 = 481.