What is 2x+1/x-3>= 2 ?

The solution to 2x+1/x-3>= 2 is 0 = (5+sqrt(17))/4

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2x+1/x-3>= 2

2 x + \frac{1}{x} - 3 \geq 2

0 < x \leq \frac{5 - 17}{4} or x \geq \frac{5 + 17}{4}

Interval Notation

(0, \frac{5 - 17}{4}] \cup [\frac{5 + 17}{4}, \infty)

Decimal Notation

0 < x \leq 0.21922 \dots or x \geq 2.28077 \dots

Solution steps

2 x + \frac{1}{x} - 3 \geq 2

Rewrite in standard form

\frac{2 x ^{2} + 1 - 5 x}{x} \geq 0

Factor

2 x^{2} + 1 - 5 x : (x - \frac{5 + 17}{4}) (x - \frac{5 - 17}{4})

\frac{( x - \frac{5 + 17}{4} ) ( x - \frac{5 - 17}{4} )}{x} \geq 0

Identify the intervals

0 < x \leq \frac{5 - 17}{4} or x \geq \frac{5 + 17}{4}

x^{2} - 3 (x^{2} - 1) = x (x - 1)

(x - 17)^{2} = 12

4 n + 2 = 5 n + 6

\frac{9}{10 k ^{4}} \cdot \frac{2 k ^{4}}{3}

\frac{2 x - 3}{7} = 3

What is 2x+1/x-3>= 2 ?
The solution to 2x+1/x-3>= 2 is 0<x<= (5-sqrt(17))/4 \lor x>= (5+sqrt(17))/4