Problem of the Week

Updated at May 22, 2023 9:05 AM

This week's problem comes from the equation category.

How would you solve \({({(u-3)}^{2}+2)}^{2}=9\)?

Let's begin!



\[{({(u-3)}^{2}+2)}^{2}=9\]

1
Take the square root of both sides.
\[{(u-3)}^{2}+2=\pm \sqrt{9}\]

2
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[{(u-3)}^{2}+2=\pm 3\]

3
Break down the problem into these 2 equations.
\[{(u-3)}^{2}+2=3\]
\[{(u-3)}^{2}+2=-3\]

4
Solve the 1st equation: \({(u-3)}^{2}+2=3\).
\[u=4,2\]

5
Solve the 2nd equation: \({(u-3)}^{2}+2=-3\).
\[u=3+\sqrt{5}\imath ,3-\sqrt{5}\imath \]

6
Collect all solutions.
\[u=4,2,3+\sqrt{5}\imath ,3-\sqrt{5}\imath \]

Done
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