Question

Find x square If x = root 5 + root 2 + root 5 - root 2 divided by root 5 + 1

Answer 1

$$\begin{gathered} Givenx=\frac{\sqrt{5}+\sqrt{2}+\sqrt{5}-\sqrt{2}}{\sqrt{5}+1} \\ \Rightarrow x=\frac{2\sqrt{5}}{\sqrt{5}+1} \\ Rationali\sin gthedenominator,weget \\ x=\frac{2\sqrt{5}}{\sqrt{5}+1}\times \frac{\sqrt{5}-1}{\sqrt{5}-1} \\ \Rightarrow x=\frac{10-2\sqrt{5}}{(\sqrt{5}{)}^2-1^2} \\ \Rightarrow x=\frac{10-2\sqrt{5}}{5-1} \\ \Rightarrow x=\frac{10-2\sqrt{5}}{4}=\frac{5-\sqrt{5}}{2} \\ \therefore x^2=(\frac{5-\sqrt{5}}{2}{)}^2=\frac{25+5-10\sqrt{5}}{4}=\frac{30-10\sqrt{5}}{4}=\frac{15-5\sqrt{5}}{2} \end{gathered}$$