Solve the inequality (1 Viewer)

[k8s]

Having trouble finding an elegant solution to this problem (if there is one) without creating a table of values.

Solve the inequation 1 + 2x -x^2 >= 2/x

This is as far as I got.... Trying to find the x intercepts of f(x) = x^2 -2x -1 + 2/x
x^2 -2x -1 + 2/x <= 0

Remove denominator by multiplying by x^2 (to ensure preservation of inequality)
x^4 -2x^3 - x^2 +2x <= 0

x(x^3 - 2x^2 - x +2) <=0

From this have (0,0) but x not = 0

 

[Drongoski]

Having trouble finding an elegant solution to this problem (if there is one) without creating a table of values.

Solve the inequation 1 + 2x -x^2 >= 2/x

This is as far as I got.... Trying to find the x intercepts of f(x) = x^2 -2x -1 + 2/x
x^2 -2x -1 + 2/x <= 0

Remove denominator by multiplying by x^2 (to ensure preservation of inequality)
x^4 -2x^3 - x^2 +2x <= 0

x(x^3 - 2x^2 - x +2) <=0

From this have (0,0) but x not = 0

 

[k8s]

Thanks heaps Drongoski. You've helped me move forward with this one.

 

[Drongoski]

Thanks heaps Drongoski. You've helped me move forward with this one.

I didn't realise until a few years ago that a Sign Diagram can be a very efficient way to solve such inequalities. It is not normally taught in the HSC.

 

[5uckerberg]

Having trouble finding an elegant solution to this problem (if there is one) without creating a table of values.

Solve the inequation 1 + 2x -x^2 >= 2/x

This is as far as I got.... Trying to find the x intercepts of f(x) = x^2 -2x -1 + 2/x
x^2 -2x -1 + 2/x <= 0

Remove denominator by multiplying by x^2 (to ensure preservation of inequality)
x^4 -2x^3 - x^2 +2x <= 0

x(x^3 - 2x^2 - x +2) <=0

From this have (0,0) but x not = 0

I mean from here you can say



Then use @Drongoski's working.