9 = 11 9=11 !!!

Level 2

Line 1: 99 = 99 99=99

Line 2: 180 − 81 = 220 − 121 180-81=220-121

Line 3: 81 − 180 = 121 − 220 81-180=121-220

Line 4: 9 2 − 2 ⋅ 9 ⋅ 10 + 1 0 2 = 1 1 2 − 2 ⋅ 11 ⋅ 10 + 1 0 2 9^2-2\cdot9\cdot10+10^2=11^2-2\cdot11\cdot10+10^2

Line 5: ( 9 − 10 ) 2 = ( 11 − 10 ) 2 (9-10)^2=(11-10)^2

Line 6: 9 − 10 = 11 − 10 9-10=11-10

Cancelling − 10 -10 from both sides, we obtain 9 = 11 9=11

In which line I did the mistake?

Line 3 Line 6 Line 4 Line 5

Rajesh Mondal by Rajesh Mondal , 30, Sweden

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2 solutions

Shikhar Jaiswal
Mar 1, 2014

he took the square root in line 6............but sqrt(x^2)=mod x...ie the positive value of x

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Aman Thegreat
Oct 21, 2017

A square root of a non negative real number can have either n e g a t i v e negative or p o s i t i v e positive real value.

That is why the anomaly arises in step 6. One cannot merely take the p o s i t i v e positive root only.

In this case, if you take the negative root of either R H S RHS or L H S LHS you obtain the correct answer.

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