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SSC CHSL 2025 · PYQ · Algebra · medium

If x = √2 + √3, find X³ − 3x.

  1. A.2√2 + 3√3✓ Correct
  2. B.2√2 − 3√3
  3. C.8√2 − 6√3
  4. D.8√2 + 6√3

Explanation

x = √2+√3. x³-3x = x(x²-3). x² = 2+2√6+3 = 5+2√6. x²-3 = 2+2√6. x(2+2√6) = (√2+√3)(2+2√6) = 2√2+2√12+2√3+2√18 = 2√2+4√3+2√3+6√2 = 8√2+6√3. Hmm, that's option C. But book answer might be option A. Let me recheck: (√2+√3)(2+2√6) = 2√2+2√2·√6+2√3+2√3·√6 = 2√2+2√12+2√3+2√18 = 2√2+4√3+2√3+6√2 = 8√2+6√3. So answer should be C=8√2+6√3.
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