Japan | A Nice Algebra Problem | Math Olympiad

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[@user-nn9gm6qk9u]

I Like your Videos

[@Light_Sound]

Sir, on what do you write these?
And also,
How can I develop such thinking so that I can solve the equations by manipulating them?
I know we require practice, but are there any more ways along with it?

[@MatthewOsterloh-gk1vt]

On the quadratic formulae inst it +1 not -1

[@user-vi8dh7gv3t]

Ответ -1.

[@SidneiMV]

2x = u => x = u/2
u³ + 2u² - 1 = 0
u³ + 1 + 2u² - 2 = 0
(u + 1)(u² - u + 1) + 2(u + 1)(u - 1) = 0
(u + 1)(u² + u - 1) = 0
u + 1 = 0 => u = -1 => *x = -1/2*
u² + u - 1 = 0
u = (-1 ± √5)/2 => *x = (-1 ± √5)/4*

[@charite7368]

X=-1/2