Problem of the Week

Updated at Jun 23, 2025 8:56 AM

For this week we've brought you this equation problem.

How would you solve \({({y}^{2}-3)}^{2}+2=38\)?

Here are the steps:



\[{({y}^{2}-3)}^{2}+2=38\]

1
Subtract \(2\) from both sides.
\[{({y}^{2}-3)}^{2}=38-2\]

2
Simplify  \(38-2\)  to  \(36\).
\[{({y}^{2}-3)}^{2}=36\]

3
Take the square root of both sides.
\[{y}^{2}-3=\pm \sqrt{36}\]

4
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[{y}^{2}-3=\pm 6\]

5
Break down the problem into these 2 equations.
\[{y}^{2}-3=6\]
\[{y}^{2}-3=-6\]

6
Solve the 1st equation: \({y}^{2}-3=6\).
\[y=\pm 3\]

7
Solve the 2nd equation: \({y}^{2}-3=-6\).
\[y=\pm \sqrt{3}\imath \]

8
Collect all solutions.
\[y=\pm 3,\pm \sqrt{3}\imath \]

Done
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