Problem of the Week

Updated at Jun 8, 2020 11:44 AM

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

How would you solve 6−(3−5u)2=26-{(3-\frac{5}{u})}^{2}=2?

Check out the solution below!



6−(3−5u)2=26-{(3-\frac{5}{u})}^{2}=2

1
Subtract 66 from both sides.
−(3−5u)2=2−6-{(3-\frac{5}{u})}^{2}=2-6

2
Simplify  2−62-6  to  −4-4.
−(3−5u)2=−4-{(3-\frac{5}{u})}^{2}=-4

3
Multiply both sides by −1-1.
(3−5u)2=4{(3-\frac{5}{u})}^{2}=4

4
Take the square root of both sides.
3−5u=±43-\frac{5}{u}=\pm \sqrt{4}

5
Since 2×2=42\times 2=4, the square root of 44 is 22.
3−5u=±23-\frac{5}{u}=\pm 2

6
Break down the problem into these 2 equations.
3−5u=23-\frac{5}{u}=2
3−5u=−23-\frac{5}{u}=-2

7
Solve the 1st equation: 3−5u=23-\frac{5}{u}=2.
u=5u=5

8
Solve the 2nd equation: 3−5u=−23-\frac{5}{u}=-2.
u=1u=1

9
Collect all solutions.
u=5,1u=5,1

Done
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