Question

If p - √q = 1/( p + √q) , where p and q are positive rational numbers , then √(q - p²) is

Answer 1

$$\begin{gathered} \mathrm{p}-\sqrt{\mathrm{q}}=\frac{1}{\mathrm{p}+\sqrt{\mathrm{q}}} \\ \left(\mathrm{p}-\sqrt{\mathrm{q}}\right)\left(\mathrm{p}+\sqrt{\mathrm{q}}\right)=1 \\ {\mathrm{p}}^2-{\left(\sqrt{\mathrm{q}}\right)}^2=1 \\ {\mathrm{p}}^2-\mathrm{q}=1 \\ -\mathrm{q}+{\mathrm{p}}^2=1 \\ \mathrm{Mutipy}\mathrm{by}-1\mathrm{both}\mathrm{side}\mathrm{we}\mathrm{get}, \\ \mathrm{q}-{\mathrm{p}}^2=-1 \\ \sqrt{\mathrm{q}-{\mathrm{p}}^2}=\sqrt{-1} \end{gathered}$$