Problem of the Week

Updated at Nov 28, 2022 11:55 AM

This week's problem comes from the equation category.

How would you solve the equation (2+4(3−u))2=36{(2+4(3-u))}^{2}=36?

Let's begin!



(2+4(3−u))2=36{(2+4(3-u))}^{2}=36

1
Factor out the common term 22.
(2(1+2(3−u)))2=36{(2(1+2(3-u)))}^{2}=36

2
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
22(1+2(3−u))2=36{2}^{2}{(1+2(3-u))}^{2}=36

3
Simplify  22{2}^{2}  to  44.
4(1+2(3−u))2=364{(1+2(3-u))}^{2}=36

4
Divide both sides by 44.
(1+2(3−u))2=364{(1+2(3-u))}^{2}=\frac{36}{4}

5
Simplify  364\frac{36}{4}  to  99.
(1+2(3−u))2=9{(1+2(3-u))}^{2}=9

6
Take the square root of both sides.
1+2(3−u)=±91+2(3-u)=\pm \sqrt{9}

7
Since 3×3=93\times 3=9, the square root of 99 is 33.
1+2(3−u)=±31+2(3-u)=\pm 3

8
Break down the problem into these 2 equations.
1+2(3−u)=31+2(3-u)=3
1+2(3−u)=−31+2(3-u)=-3

9
Solve the 1st equation: 1+2(3−u)=31+2(3-u)=3.
u=2u=2

10
Solve the 2nd equation: 1+2(3−u)=−31+2(3-u)=-3.
u=5u=5

11
Collect all solutions.
u=2,5u=2,5

Done
Cymath foriOSAndroid