Problem of the Week

Updated at Jul 8, 2019 5:12 PM

How can we solve the equation $$4{u}^{2}-\frac{20}{u}=59$$?

Below is the solution.

$4{u}^{2}-\frac{20}{u}=59$

1
Multiply both sides by $$u$$.
$4{u}^{3}-20=59u$

2
Move all terms to one side.
$4{u}^{3}-20-59u=0$

3
Factor $$4{u}^{3}-20-59u$$ using Polynomial Division.
$(4{u}^{2}+16u+5)(u-4)=0$

4
Solve for $$u$$.
$u=4$

5
$u=\frac{-16+4\sqrt{11}}{8},\frac{-16-4\sqrt{11}}{8}$
$u=4,\frac{-16+4\sqrt{11}}{8},\frac{-16-4\sqrt{11}}{8}$
$u=4,-\frac{4-\sqrt{11}}{2},-\frac{4+\sqrt{11}}{2}$