Problem of the Week

Updated at Aug 1, 2022 12:33 PM

This week we have another equation problem:

How can we solve the equation (n5−3)2−3=1{(\frac{n}{5}-3)}^{2}-3=1?

Let's start!



(n5−3)2−3=1{(\frac{n}{5}-3)}^{2}-3=1

1
Add 33 to both sides.
(n5−3)2=1+3{(\frac{n}{5}-3)}^{2}=1+3

2
Simplify  1+31+3  to  44.
(n5−3)2=4{(\frac{n}{5}-3)}^{2}=4

3
Take the square root of both sides.
n5−3=±4\frac{n}{5}-3=\pm \sqrt{4}

4
Since 2×2=42\times 2=4, the square root of 44 is 22.
n5−3=±2\frac{n}{5}-3=\pm 2

5
Break down the problem into these 2 equations.
n5−3=2\frac{n}{5}-3=2
n5−3=−2\frac{n}{5}-3=-2

6
Solve the 1st equation: n5−3=2\frac{n}{5}-3=2.
n=25n=25

7
Solve the 2nd equation: n5−3=−2\frac{n}{5}-3=-2.
n=5n=5

8
Collect all solutions.
n=25,5n=25,5

Done
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