Math Olympiad | Solve for X | Important Geometry skills explained

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[@rajanrg]

This is Algebra plus Geometry i.e. Analytical Geometry. I also refreshed my intermediate school knowledge. thanks

[@vijaymaths5483]

Most welcome

[@Rocio62154]

EXCELLENTONIO

[@RyanLewis-Johnson-wq6xs]

m=(-(-1)+sqrt((-1)^2-4(1)(-1))/(2*1)=(1+sqrt(5))/2=0.5+0.5sqrt(5) m=(1-sqrt(5))/2 m=0.5-0.5sqrt(5)

[@RyanLewis-Johnson-wq6xs]

Input
sqrt(1/2 (1 + sqrt(5))) = 0.5 sqrt(2 + 2 sqrt(5))
Result
True
Left hand side
sqrt(1/2 (1 + sqrt(5))) = 1/2 sqrt((1 + sqrt(5)) 2)
Right hand side
0.5 sqrt(2 + 2 sqrt(5)) = 1/2 sqrt((1 + sqrt(5)) 2)=x

[@RyanLewis-Johnson-wq6xs]

Sqrt[(1-Sqrt[5])/2]=0.5Sqrt[2Sqrt[5]-2]i

[@Danieswors]

1.2720

m is golden ratio.

[@vijaymaths5483]

Yes 👍

[@RealQinnMalloryu4]

(x^3)^2=x^9 (x^2)^2=x^4 {x^9+x^4}= x^13 (x)^2=x^2 x^13/x^2= 6.1 3^2.1^1 3^2(x ➖ 3x±2).