Question

\[x ^{-2}-4x ^{-1}=0\]

Help me

Answer 1

This can be rewritten as \[1/x^2-1/4x=0\]
If you plug this into a TI-89 using the solve function, you get: \[x=1/4\]
Hope this helps.

Answer 2

factor the left side into
\[\frac{1}{x}(\frac{1}{x}-4)=0\]and set the factors equal to zero.
\[\frac{1}{x}=0\] is not true for any real x, so this gives no solutions.
\[\frac{1}{x}-4=0\] gives
\[\frac{1}{x}=4\]and so, multiplying both sides by x and dividing by 4,
\[x=\frac{1}{4}\]

Answer 3

got this one :)

Answer 4

\[\frac{1}{x ^{2}}-\frac{4}{x}=10\]\[Denominator is: x ^{2}\]\[\frac{1*x}{x ^{2}}-\frac{4*x}{x*x}=10*x^2\]get rid with denominator\[1-4x=10x ^{2}\]\[10x ^{2}-4x+1=0\]\[\frac{-(-4)\pm \sqrt{-4^{2}-(-4\times10\times1)}}{2\times10}\]\[\frac{4\pm \sqrt{16+40}}{20}\]\[\frac{4\pm 2\sqrt{14}}{20}\]\[\frac{2\pm \sqrt{14}}{10}\]