Question

-80=-80,
100-180+81=64-144+81
10^2-2*10*9+9^2=8^2-2*8*9+9^2
(10-9)^2=(8-9)^2
10-9=8-9(taking positive square root)
So, 10=9 i.e. 2=1 What is the falacy?

Answer 1

(8-9)^2 =1 ---8^2+9^2 ≠1

Answer 2

(8-9)^2=8^2+9^2-2*8*9=1

Answer 3

second to the last line where you took the square roots of both sides should end up with the equality (10-9)=(9-8) because in the line above that, you're taking the principle (positive) square root. So the original equality of 10-9=8-9 is wrong obviously because the left side of the equal sign is positive but the right side is negative.