Question

If square root of 2 + square root of xis equal to 3, then what is x equal to ?

Answer 1

$$\begin{gathered} \sqrt{2}+\sqrt{x}=3 \\ \Rightarrow \sqrt{x}=3-\sqrt{2} \\ \Rightarrow x={\left(3-\sqrt{2}\right)}^2\{\mathrm{Squaring}\mathrm{both}\mathrm{sides}\} \\ \Rightarrow x=3^2+{\left(\sqrt{2}\right)}^2-2\times 3\times \sqrt{2}\{\mathrm{using}\mathrm{the}\mathrm{identity}{\left(\mathrm{a}-\mathrm{b}\right)}^2={\mathrm{a}}^2+{\mathrm{b}}^2-2\mathrm{ab}\} \\ \Rightarrow x=9+2-6\sqrt{2}=11-6\sqrt{2} \end{gathered}$$