Problem of the Week

Updated at May 22, 2023 9:05 AM

This week's problem comes from the equation category.

How would you solve ((u−3)2+2)2=9{({(u-3)}^{2}+2)}^{2}=9?

Let's begin!



((u−3)2+2)2=9{({(u-3)}^{2}+2)}^{2}=9

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

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

3
Break down the problem into these 2 equations.
(u−3)2+2=3{(u-3)}^{2}+2=3
(u−3)2+2=−3{(u-3)}^{2}+2=-3

4
Solve the 1st equation: (u−3)2+2=3{(u-3)}^{2}+2=3.
u=4,2u=4,2

5
Solve the 2nd equation: (u−3)2+2=−3{(u-3)}^{2}+2=-3.
u=3+5ı,3−5ıu=3+\sqrt{5}\imath ,3-\sqrt{5}\imath

6
Collect all solutions.
u=4,2,3+5ı,3−5ıu=4,2,3+\sqrt{5}\imath ,3-\sqrt{5}\imath

Done
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