Problem of the Week

Updated at Feb 17, 2025 11:31 AM

For this week we've brought you this equation problem.

How would you solve the equation ((u+2)26)2=649{(\frac{{(u+2)}^{2}}{6})}^{2}=\frac{64}{9}?

Here are the steps:



((u+2)26)2=649{(\frac{{(u+2)}^{2}}{6})}^{2}=\frac{64}{9}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
((u+2)2)262=649\frac{{({(u+2)}^{2})}^{2}}{{6}^{2}}=\frac{64}{9}

2
Use Power Rule: (xa)b=xab{({x}^{a})}^{b}={x}^{ab}.
(u+2)462=649\frac{{(u+2)}^{4}}{{6}^{2}}=\frac{64}{9}

3
Simplify  62{6}^{2}  to  3636.
(u+2)436=649\frac{{(u+2)}^{4}}{36}=\frac{64}{9}

4
Multiply both sides by 3636.
(u+2)4=649×36{(u+2)}^{4}=\frac{64}{9}\times 36

5
Use this rule: ab×c=acb\frac{a}{b} \times c=\frac{ac}{b}.
(u+2)4=64×369{(u+2)}^{4}=\frac{64\times 36}{9}

6
Simplify  64×3664\times 36  to  23042304.
(u+2)4=23049{(u+2)}^{4}=\frac{2304}{9}

7
Simplify  23049\frac{2304}{9}  to  256256.
(u+2)4=256{(u+2)}^{4}=256

8
Take the 44th root of both sides.
u+2=±2564u+2=\pm \sqrt[4]{256}

9
Calculate.
u+2=±4u+2=\pm 4

10
Break down the problem into these 2 equations.
u+2=4u+2=4
u+2=−4u+2=-4

11
Solve the 1st equation: u+2=4u+2=4.
u=2u=2

12
Solve the 2nd equation: u+2=−4u+2=-4.
u=−6u=-6

13
Collect all solutions.
u=2,−6u=2,-6

Done
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