Solve For x

[nycmathguy]

David Cohen questions just for fun.
Enjoy.

 

[MathLover1]

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

 

[nycmathguy]

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

Thank you. I know you like the David Cohen book, right? Great math work here.