Sweden | A Nice Algebra Problem | Math Olympiad

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[@willberry3199]

There are three solutions. It is valid for "t" to be negative because we are solving for x, not for its square root. Continuing that third line we end up with x = (3 - sqrt(5)) / 2 which can be verified in the original equation without any square roots of negative numbers.

[@seringoften]

can you explain it more simply sorry i don't understand to that 😅

[@willberry3199]

@@seringoften In the video he stopped calculating one solution after finding t was negative, but he should have kept going, it leads to a third valid solution.

[@oleglevchenko907]

No, x = (3 - sqrt(5)) / 2 ≈ 0.382 is NOT solution. Just try to verify it with a calculator: x*sqrt(x)≈0.236, and x+sqrt(x)=1.

[@gloystar]

Solved it before playing the video in exactly the same way. Turned out the solutions were (zero) and the (square of the golden ratio). Great video.

[@napoleonjr.gaquing379]

Squaring of the RHS is incorrect.

[@Nguyễn-j9q]

X=0

[@Patrik6920]

and 2x = 3+√5

[@Baltie3]

This is not an olympiad level.