What is 5x^6-x^4>5x^5 ?

The solution to 5x^6-x^4>5x^5 is x (3+sqrt(5))/(2sqrt(5))

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5x^6-x^4>5x^5

5 x^{6} - x^{4} > 5 x^{5}

x < \frac{5 - 3}{2 5} or x > \frac{3 + 5}{2 5}

Interval Notation

(- \infty, \frac{5 - 3}{2 5}) \cup (\frac{3 + 5}{2 5}, \infty)

Decimal Notation

x < - 0.17082 \dots or x > 1.17082 \dots

Solution steps

5 x^{6} - x^{4} > 5 x^{5}

Rewrite in standard form

5 x^{6} - x^{4} - 5 x^{5} > 0

Factor

5 x^{6} - x^{4} - 5 x^{5} : x^{4} (x - \frac{5 + 3}{2 5}) (x - \frac{5 - 3}{2 5})

x^{4} (x - \frac{5 + 3}{2 5}) (x - \frac{5 - 3}{2 5}) > 0

Identify the intervals

x < \frac{5 - 3}{2 5} or x > \frac{3 + 5}{2 5}

\frac{1}{x} + \frac{1}{x} - 1 + \frac{1}{x} - 2 > 0

x^{2} + 4 x + 1 \geq - 3

n^{4} + 6 n^{3} + 6 n^{2} + 6 n + 5 < 0

\frac{( 2 x - 3 )}{( x - 1 )} \leq 2

4 x^{2} - 4 < x^{2} - x

What is 5x^6-x^4>5x^5 ?
The solution to 5x^6-x^4>5x^5 is x<(sqrt(5)-3)/(2sqrt(5))\lor x>(3+sqrt(5))/(2sqrt(5))