A very nice math olympiad question || Surprisingly easy || You should know this trick || Algebra

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  • Опубліковано 20 сер 2024
  • See the way I breakdown the solution of this question. There is a lot you can learn from this video.
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КОМЕНТАРІ • 3

  • @danmimis4576
    @danmimis4576 Місяць тому

    What's wrong with √1 = -1?

  • @SidneiMV
    @SidneiMV Місяць тому +1

    [1 + √(1 + x)]³ = x²
    √(1 + x) = u
    1 + x = u² => x = u² - 1
    (u + 1)³ = (u² - 1)²
    (u + 1)²(u + 1) = (u + 1)²(u - 1)²
    (u + 1)²[u + 1 - (u - 1)²] = 0
    (u + 1)²(u² - 3u) = 0
    u(u + 1)²(u - 3) = 0
    u = 0 => x = -1 (not valid)
    u = -1 => x = 0 (not valid)
    u = 3 => *x = 8*