Problem of the Week

Updated at Mar 4, 2024 2:14 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve \(2+{(3-\frac{5}{u})}^{2}=\frac{34}{9}\)?

Check out the solution below!



\[2+{(3-\frac{5}{u})}^{2}=\frac{34}{9}\]

1
Subtract \(2\) from both sides.
\[{(3-\frac{5}{u})}^{2}=\frac{34}{9}-2\]

2
Simplify  \(\frac{34}{9}-2\)  to  \(\frac{16}{9}\).
\[{(3-\frac{5}{u})}^{2}=\frac{16}{9}\]

3
Take the square root of both sides.
\[3-\frac{5}{u}=\pm \sqrt{\frac{16}{9}}\]

4
Simplify  \(\sqrt{\frac{16}{9}}\)  to  \(\frac{\sqrt{16}}{\sqrt{9}}\).
\[3-\frac{5}{u}=\pm \frac{\sqrt{16}}{\sqrt{9}}\]

5
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[3-\frac{5}{u}=\pm \frac{4}{\sqrt{9}}\]

6
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[3-\frac{5}{u}=\pm \frac{4}{3}\]

7
Break down the problem into these 2 equations.
\[3-\frac{5}{u}=\frac{4}{3}\]
\[3-\frac{5}{u}=-\frac{4}{3}\]

8
Solve the 1st equation: \(3-\frac{5}{u}=\frac{4}{3}\).
\[u=3\]

9
Solve the 2nd equation: \(3-\frac{5}{u}=-\frac{4}{3}\).
\[u=\frac{15}{13}\]

10
Collect all solutions.
\[u=3,\frac{15}{13}\]

Done

Decimal Form: 3, 1.153846
Cymath foriOSAndroid