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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What's wrong with √1 = -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*
Excellent!!!