Question

Find error.. in the given solution<br />$we \: know \: that \\ 2 + 2 = 4 \\ which \: gives - \\ \: \: \: \: \: \: 2 + 2 = 4 - \binom{9}{2} + \binom{9}{2} \\ or \: \: 2 + 2 = \sqrt{4 -(9 \div 2) }^{2} +\binom{9}{2}\\ or \: 2 + 2 = \sqrt{16 - 36 + (81 \div 4)} + \binom{9}{2} \\ or \: 2 + 2 = \sqrt{ - 20 + (81 \div 4)} + \binom{9}{2} \\ or \: 2 + 2 = \sqrt{25 - 45 + (81 \div 4)} + \binom{9}{2} \\ or \: 2 + 2 = \sqrt{ {5}^{2} - 45 + {(9 \div 2)}^{2} } + \binom{9}{2} \\ or \: 2 + 2 = \sqrt{5 - (9 \div 2) }^{2} + \binom{9}{2} \\ or \: 2 + 2 = 5 - \binom{9}{2} + \binom{9}{2} \\ or \: 2 + 2 = 5 \\ hence \: proved$

Answer 1

For reference, the most serious mistake was in the 2nd line. In general, it's not true that √x^2=x rather √x^2=|x| For x=4−9/2<0. x=4−9/2<0, you need to keep track of the extra minus sign coming from the absolute value.
square root of negative can't be takeni
ik the first line you have
$4 - 4.5 = \sqrt{ {(4 - 4.5)}^{2} } \\ - 0.5 = 0.5$
how it can be possible