So long

Algebra Level 3

How many real solutions does this equation have?

$x^9+18x^6+108x^3=\sqrt{x-6}$

The answer is 0.

1 solution

Steven Jim
Nov 20, 2017

Intuitively, one may find that $x \ge 6$ (of course the left side is real, so we can say the right one must also be) and that for $x \ge 6$ , $x^9>x^{1/2}>{(x-6)}^{1/2}$ . Thus, no solution.

Anyways, you might want to use this version ( $LaTeX$ used), your choice though: $x^9+18x^6+108x^3={(x-6)}^{1/2}$ .

Use "Toggle LaTeX" on your upper right to copy.

Steven Jim - 3 years, 6 months ago

So long

The answer is 0.

1 solution

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