Conquer Math Olympiad:Master Easy Solutions To Questions!!

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Learn How To Solve|Find The Value|Math Olympiad Questions!!
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Hi friends ,
Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy method.

Learn how to solve the olympiad question quickly with tips and tricks which are very easy to understand.

International ,national,regional math olympiad hard question and solutions for our beloved subscribers and wellwishers to secure knowledge and get ranks in all the olympiad maths Competitions.

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[sanjaysurya]

I love tough, challenging problems... Nice problem 💯

[guyhoghton]

We get an alternative route if we rearrange the equation first.
_∛(x + 1) - ∛x = ∛(x³ - x + 1) - ∛(x³ - x)_ ... ①
C.B.S:
_1 - 3∛( x(x + 1) )( ∛(x + 1) - ∛x ) = 1 - 3∛( (x³ - x + 1)(x³ - x) )( ∛(x³ - x + 1) - ∛(x³ - x) )_
∴ _∛( x(x + 1) )( ∛(x + 1) - ∛x ) = ∛( (x³ - x + 1)(x³ - x) )( ∛(x³ - x + 1) - ∛(x³ - x) )_ ...②
Since _∛(x + 1) ≠ ∛x_
both sides of ① ≠ 0 and they can be respectively cancelled from either side of ②.
∴ _∛( x(x + 1) ) = ∛( (x³ - x + 1)(x³ - x) )_
∴ _x(x + 1) = (x³ - x + 1)x(x + 1)(x - 1)_
∴ _x(x + 1)[(x³ - x + 1)(x - 1) - 1] = 0_
∴ _x(x + 1)(x⁴ - x³ - x² + 2x - 2) = 0_
∴ _x(x + 1)(x² - x + 1)(x² - 2) = 0_
↑ ↑ ↑ ↑
_x = 0, x = -1, Δ = -3, x = ±√2_