Smart problem

Algebra Level pending

1) -20=-20

2) 16-36=25-45

3) 16-36+ 81 4 \frac{81}{4} =25-45+ 81 4 \frac{81}{4}

4) 4^{2}+( 9 2 \frac{9}{2} )^{2}-2x4x 9 2 \frac{9}{2} =5^{2}+( 9 2 \frac{9}{2} )^{2}-2x5x 9 2 \frac{9}{2}

5) (4- 9 2 \frac{9}{2} )^{2}=(5- 9 2 \frac{9}{2} )^{2}

6) ((4- 9 2 \frac{9}{2} )^{2})^{0.5}=((5- 9 2 \frac{9}{2} )^{2})^{0.5}

7) 4- 9 2 \frac{9}{2} =5- 9 2 \frac{9}{2}

8) 4=5

9) 2+2=5

Where is the first mistake occurs?

None of the choices 4 2 5

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1 solution

Joshua Chin
Mar 30, 2016

When squarerooting, one obtains the positive value. Thus step 6 is the error, as 4 9 2 < 0 4-\frac {9}{2}<0 . In fact, step 7 should be 4 9 2 = 5 9 2 |4-\frac {9}{2}|=5-\frac {9}{2} , which is true.

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