4 = 5 ! Που βρίσκεται το λάθος ;

$4=2+2$

$=4-{\displaystyle \frac{9}{2}}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(4-{\displaystyle \frac{9}{2}}{)}^2}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(16-2\cdot 4\cdot {\displaystyle \frac{9}{2}}+({\displaystyle \frac{9}{2}}{)}^2)}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(16-36+({\displaystyle \frac{9}{2}}{)}^2)}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(-20+({\displaystyle \frac{9}{2}}{)}^2)}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(25-45+({\displaystyle \frac{9}{2}}{)}^2)}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(5^2-2\cdot 5\cdot {\displaystyle \frac{9}{2}}+({\displaystyle \frac{9}{2}}{)}^2)}+{\displaystyle \frac{9}{2}}$

$=\sqrt{(5-{\displaystyle \frac{9}{2}}{)}^2}+{\displaystyle \frac{9}{2}}$

$=5-{\displaystyle \frac{9}{2}}+{\displaystyle \frac{9}{2}}$

$=5$