Question

If x+1/x=6   then 

x  =

ahhh im stuck on this one!!

Answer 1

`(x+1)/(x)=6|*x`

`x\\eq6`

`x+1=6x`

`1=5x|:5`

`x=(1)/(5)=0.2`

Answer 2

`x+(1)/(x)=6;\ D:x\\eq0\\\\(x^2)/(x)+(1)/(x)=6\\\\(x^2+1)/(x)=(6)/(1)\\\\cross\ multiply\\\\x^2+1=6x\\\\x^2-6x+1=0\\\\x^2-2x(3)+3^2-3^2+1=0`


`(x-3)^2-9+1=0\\\\(x-3)^2-8=0\\\\(x-3)^2=8\iff x-3=\sqrt8\ or\ x-3=-\sqrt8\\\\x=3+√(4\cdot2)\ or\ x=3-√(4\cdot2)\\\\\boxed{x=3+2\sqrt2\ or\ x=3-2\sqrt2}`

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`if:\\\\(x+1)/(x)=6;\ D:x\\eq0\\\\(x+1)/(x)=(6)/(1)\\\\cross\ multiply\\\\6x=x+1\\\\6x-x=1\\\\5x=1\ \ \ \ \ |:5\\\\\boxed{x=(1)/(5)}`