Question

factorise x²+5x-1 using suitable identity

Answer 1

$$\begin{gathered} {\mathrm{x}}^2+5\mathrm{x}-1 \\ ={\mathrm{x}}^2+5\mathrm{x}+\frac{25}{4}-\frac{25}{4}-1 \\ ={\left(\mathrm{x}+\frac{5}{2}\right)}^2-\frac{29}{4} \\ ={\left(\mathrm{x}+\frac{5}{2}\right)}^2-{\left(\frac{\sqrt{29}}{2}\right)}^2 \\ =\left(\mathrm{x}+\frac{5}{2}-\frac{\sqrt{29}}{2}\right)\left(\mathrm{x}+\frac{5}{2}+\frac{\sqrt{29}}{2}\right) \\ =\left(\mathrm{x}+\frac{5-\sqrt{29}}{2}\right)\left(\mathrm{x}+\frac{5+\sqrt{29}}{2}\right) \end{gathered}$$