Problem of the Week

Updated at Mar 22, 2021 2:49 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation 33−(5m)2=32\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}?

Check out the solution below!



33−(5m)2=32\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
33−52m2=32\frac{3}{3-\frac{{5}^{2}}{{m}^{2}}}=\frac{3}{2}

2
Simplify  52{5}^{2}  to  2525.
33−25m2=32\frac{3}{3-\frac{25}{{m}^{2}}}=\frac{3}{2}

3
Multiply both sides by 3−25m23-\frac{25}{{m}^{2}}.
3=32(3−25m2)3=\frac{3}{2}(3-\frac{25}{{m}^{2}})

4
Divide both sides by 33.
1=12(3−25m2)1=\frac{1}{2}(3-\frac{25}{{m}^{2}})

5
Simplify  3−25m22\frac{3-\frac{25}{{m}^{2}}}{2}  to  32−25m22\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}.
1=32−25m221=\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}

6
Simplify  25m22\frac{\frac{25}{{m}^{2}}}{2}  to  252m2\frac{25}{2{m}^{2}}.
1=32−252m21=\frac{3}{2}-\frac{25}{2{m}^{2}}

7
Subtract 32\frac{3}{2} from both sides.
1−32=−252m21-\frac{3}{2}=-\frac{25}{2{m}^{2}}

8
Simplify  1−321-\frac{3}{2}  to  −12-\frac{1}{2}.
−12=−252m2-\frac{1}{2}=-\frac{25}{2{m}^{2}}

9
Multiply both sides by 2m22{m}^{2}.
−12×2m2=−25-\frac{1}{2}\times 2{m}^{2}=-25

10
Cancel 22.
−m2=−25-{m}^{2}=-25

11
Multiply both sides by −1-1.
m2=25{m}^{2}=25

12
Take the square root of both sides.
m=±25m=\pm \sqrt{25}

13
Since 5×5=255\times 5=25, the square root of 2525 is 55.
m=±5m=\pm 5

Done
Cymath foriOSAndroid