How this process has been calculated in a manner added.
$$\begin{align} 2+2 &amp;= 4 - \frac92 +\frac92\\ &amp;= \sqrt{\left(4-\frac92\right)^2} +\frac92\\ &amp;= \sqrt{16 -2\times4\times\frac92 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{16 -36 + \left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {-20 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{25-45 +\left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {5^2 -2\times5\times\frac92 + \left(\frac92\right) ^2} + \frac92\\ &amp;= \sqrt {\left(5-\frac92\right)^2} +\frac92\\ &amp;= 5 + \frac92 - \frac92 \\ &amp;= 5\end{align}$$  Where did I go wrong
Why does one often see "null != variable" instead of "variable != null" in C#? mbstring is missing for phpmyadmin in ubuntu 16.04 When I installed phpmyadmin in Ubuntu 16.04 LTS, it gives me an error mentioned below.     The mbstring extension is missing. Please check your PHP configuration   then I tried to install php-mbstring, it says mbstring is up to date, Can anyone help me to solve this? If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined From Ireland,Rosen's Number Theory book, ex.8.12.  Let $p\equiv1\mod{4}$, then we can write $p=a^{2}+b^{2}$, where $a,b\in\mathbb{Z}$. Now, let $a$ be odd and $b$ be even and $a,b&gt;0$. How can we show that $a$ and $b$ are uniquely determined? The hint says to use the fact that $\mathbb{Z[i]}$ is a UFD and $p=a^{2}+b^{2}\implies a+bi$ is prime in $\mathbb{Z[i]}$ Problem understanding the logistic regression link function Why can a discontinuous function not be differentiable? 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