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David Cohen questions just for fun.
Enjoy.
Enjoy.
x+12/x=(sqrt(x)-sqrt(12/x))^2+2sqrt(12)
x+12/x=(sqrt(x))^2-2sqrt(x)sqrt(12/x)+(sqrt(12/x))^2+2sqrt(12)
x+12/x=x-2sqrt(x)sqrt(12/x)+12/x+2sqrt(12).......simplify
0=-2sqrt(x)sqrt(12/x)+2sqrt(12)
0=-2(sqrt(x)sqrt(12/x)-sqrt(12))
0=-2(2sqrt(3) sqrt(1/x) sqrt(x)-2sqrt(3))
0=-2*2sqrt(3)( sqrt(1/x) sqrt(x)-1)
0=-4sqrt(3)( sqrt(1/x) sqrt(x)-1)..........will be equal to zero only if
sqrt(1/x) sqrt(x)-1=0
sqrt(1/x) sqrt(x)=1 ........square both sides
(1/x) x=1
x/x=1.........will be true only if =>x=1