Answer:
[tex]\mathrm{1.\: x=-1\pm\sqrt{2}}[/tex][tex]\mathrm{2.\: x=-3 \pm 2\sqrt{5}}[/tex][tex]\mathrm{3.\: x=-1 \pm \sqrt{2}}[/tex]
Step-by-step explanation:
[tex]\mathrm{1.\: x^2+2x-1=0}\\\\\mathrm{=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-1\right)}}{2\cdot \:1}}\\\\\mathrm{=\frac{-2\pm \:2\sqrt{2}}{2\cdot \:1}}\\\\\mathrm{x_1=\frac{-2+2\sqrt{2}}{2\cdot \:1},\:x_2=\frac{-2-2\sqrt{2}}{2\cdot \:1}}\\\\\mathrm{x=-1\pm\sqrt{2}}[/tex]
[tex]\mathrm{2.\: x^2+6x-11=0}\\\\\mathrm{=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1}}\\\\\mathrm{x_1=\frac{-6+4\sqrt{5}}{2\cdot \:1},\:x_2=\frac{-6-4\sqrt{5}}{2\cdot \:1}}\\\\\mathrm{x=-3 \pm 2\sqrt{5}}[/tex]
[tex]\mathrm{3.\: 2x^2+4x-2=0}\\\\\mathrm{=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-2\right)}}{2\cdot \:2}}\\\\\mathrm{=\frac{-4\pm \:4\sqrt{2}}{2\cdot \:2}}\\\\\mathrm{x_1=\frac{-4+4\sqrt{2}}{2\cdot \:2},\:x_2=\frac{-4-4\sqrt{2}}{2\cdot \:2}}\\\\\mathrm{x=-1 \pm \sqrt{2}}[/tex]