Problem of the Week

Updated at Feb 14, 2022 8:30 AM

This week's problem comes from the equation category.

How can we solve the equation \(\frac{{({p}^{2}-3)}^{2}}{5}=\frac{1}{5}\)?

Let's begin!



\[\frac{{({p}^{2}-3)}^{2}}{5}=\frac{1}{5}\]

1
Multiply both sides by \(5\).
\[{({p}^{2}-3)}^{2}=\frac{1}{5}\times 5\]

2
Cancel \(5\).
\[{({p}^{2}-3)}^{2}=1\]

3
Take the square root of both sides.
\[{p}^{2}-3=\pm \sqrt{1}\]

4
Simplify  \(\sqrt{1}\)  to  \(1\).
\[{p}^{2}-3=\pm 1\]

5
Break down the problem into these 2 equations.
\[{p}^{2}-3=1\]
\[{p}^{2}-3=-1\]

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

7
Solve the 2nd equation: \({p}^{2}-3=-1\).
\[p=\pm \sqrt{2}\]

8
Collect all solutions.
\[p=\pm 2,\pm \sqrt{2}\]

Done

Decimal Form: ±2, ±1.414214
Cymath foriOSAndroid