2 + 2 = 5

Algebra Level 2

Below is the "proof" that 2 + 2 = 5. 2 + 2 = 5.

Step 1: 2 + 2 = 4 2 + 2 = 4
Step 2: = 4 − 9 2 + 9 2 = 4 - {\frac{9}{2}} + {\frac{9}{2}}
Step 3: = ( 4 − 9 2 ) 2 + 9 2 = \sqrt{(4 - {\frac{9}{2}})^2} + {\frac{9}{2}}
Step 4: = 16 − 2 × 4 × 9 2 + ( 9 2 ) 2 + 9 2 = \sqrt{16 - 2 \times 4 \times {\frac{9}{2}} + {(\frac{9}{2})^2}} + {\frac{9}{2}}
Step 5: = − 20 + ( 9 2 ) 2 + 9 2 = \sqrt{-20 + {(\frac{9}{2})^2}} + {\frac{9}{2}}
Step 6: = 25 − 45 + ( 9 2 ) 2 + 9 2 = \sqrt{25 - 45 + {(\frac{9}{2})^2}} + {\frac{9}{2}}
Step 7: = 5 2 − 2 × 5 × 9 2 + ( 9 2 ) 2 + 9 2 = \sqrt{5^2 - 2 \times 5 \times {\frac{9}{2}} + {(\frac{9}{2})^2}} + {\frac{9}{2}}
Step 8: = ( 5 − 9 2 ) 2 + 9 2 = \sqrt{(5 -{\frac{9}{2}})^2} + {\frac{9}{2}}
Step 9: 2 + 2 = 5 − 9 2 + 9 2 2 + 2 = 5 - {\frac{9}{2}} + {\frac{9}{2}}
Step 10: 2 + 2 = 5 \boxed{2 + 2 = 5}

In which step there is the first flaw?

Bonus: What alteration can you make in order to correct this flaw?
4 3 7 5 8 6 2

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Naren Bhandari
Feb 5, 2018

In step 3 ( 4 − 9 2 ) 2 = ∣ 4 − 9 2 ∣ = 9 2 − 4 \begin{aligned} \sqrt{\left(4-\frac{9}{2}\right)^2} = \big| 4-\frac{9}{2}\big | = \frac{9}{2} -4 \end{aligned}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...