Problem of the Week

Updated at Feb 28, 2022 12:38 PM

This week we have another equation problem:

How would you solve (u+22)25=95\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}?

Let's start!



(u+22)25=95\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}

1
Simplify  u+22\frac{u+2}{2}  to  1+u21+\frac{u}{2}.
(1+u2)25=95\frac{{(1+\frac{u}{2})}^{2}}{5}=\frac{9}{5}

2
Multiply both sides by 55.
(1+u2)2=95×5{(1+\frac{u}{2})}^{2}=\frac{9}{5}\times 5

3
Cancel 55.
(1+u2)2=9{(1+\frac{u}{2})}^{2}=9

4
Take the square root of both sides.
1+u2=±91+\frac{u}{2}=\pm \sqrt{9}

5
Since 3×3=93\times 3=9, the square root of 99 is 33.
1+u2=±31+\frac{u}{2}=\pm 3

6
Break down the problem into these 2 equations.
1+u2=31+\frac{u}{2}=3
1+u2=−31+\frac{u}{2}=-3

7
Solve the 1st equation: 1+u2=31+\frac{u}{2}=3.
u=4u=4

8
Solve the 2nd equation: 1+u2=−31+\frac{u}{2}=-3.
u=−8u=-8

9
Collect all solutions.
u=4,−8u=4,-8

Done
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