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9)
![x^2-4x+1=0;\ sqrt{x_1}+sqrt{x_2}-?;\
x_1cdot x_2=1;\
x_1+x_2=4;\
D=16-4=12;\
x_1=frac{4-2sqrt3}{2} =2-sqrt{3};\
x_2=frac{4+2sqrt3}{2}=2+sqrt3;\
sqrt{x_1}+sqrt{x_2}=sqrt{(sqrt{x_1}+sqrt{x_2})^2}=sqrt{(x_1+2cdotsqrt{x_1}cdotsqrt{x_2}+x_2)}=\
=sqrt{(x_1+x_2)+2sqrt{x_1cdot x_2}}=sqrt{4+2cdotsqrt1}=sqrt{4+2}=sqrt{6};\
sqrt{x_1}+sqrt{x_2}=sqrt6](https://tex.z-dn.net/?f=x%5E2-4x%2B1%3D0%3B%5C+sqrt%7Bx_1%7D%2Bsqrt%7Bx_2%7D-%3F%3B%5C+%0Ax_1cdot+x_2%3D1%3B%5C+%0Ax_1%2Bx_2%3D4%3B%5C+%0AD%3D16-4%3D12%3B%5C%0Ax_1%3Dfrac%7B4-2sqrt3%7D%7B2%7D+%3D2-sqrt%7B3%7D%3B%5C+%0Ax_2%3Dfrac%7B4%2B2sqrt3%7D%7B2%7D%3D2%2Bsqrt3%3B%5C%0Asqrt%7Bx_1%7D%2Bsqrt%7Bx_2%7D%3Dsqrt%7B%28sqrt%7Bx_1%7D%2Bsqrt%7Bx_2%7D%29%5E2%7D%3Dsqrt%7B%28x_1%2B2cdotsqrt%7Bx_1%7Dcdotsqrt%7Bx_2%7D%2Bx_2%29%7D%3D%5C%0A%3Dsqrt%7B%28x_1%2Bx_2%29%2B2sqrt%7Bx_1cdot+x_2%7D%7D%3Dsqrt%7B4%2B2cdotsqrt1%7D%3Dsqrt%7B4%2B2%7D%3Dsqrt%7B6%7D%3B%5C%0Asqrt%7Bx_1%7D%2Bsqrt%7Bx_2%7D%3Dsqrt6 "x^2-4x+1=0;\ sqrt{x_1}+sqrt{x_2}-?;\
x_1cdot x_2=1;\
x_1+x_2=4;\
D=16-4=12;\
x_1=frac{4-2sqrt3}{2} =2-sqrt{3};\
x_2=frac{4+2sqrt3}{2}=2+sqrt3;\
sqrt{x_1}+sqrt{x_2}=sqrt{(sqrt{x_1}+sqrt{x_2})^2}=sqrt{(x_1+2cdotsqrt{x_1}cdotsqrt{x_2}+x_2)}=\
=sqrt{(x_1+x_2)+2sqrt{x_1cdot x_2}}=sqrt{4+2cdotsqrt1}=sqrt{4+2}=sqrt{6};\
sqrt{x_1}+sqrt{x_2}=sqrt6")
12)
![x^2-(2+3sqrt2)x+6sqrt2=0;\ D=(2+3sqrt2)^2-24sqrt2=4+12sqrt2+18-24sqrt2=4-<br />12sqrt2+18=\ =(2-3sqrt2)^2;\ x_1=frac{2+3sqrt2-2+3sqrt2}{2}=frac{6sqrt2}{2}=3sqrt2;\ x_2=frac{2+3sqrt2+2-3sqrt2}{2}=frac{4}{2}=2;\](https://tex.z-dn.net/?f=x%5E2-%282%2B3sqrt2%29x%2B6sqrt2%3D0%3B%5C+D%3D%282%2B3sqrt2%29%5E2-24sqrt2%3D4%2B12sqrt2%2B18-24sqrt2%3D4-%26lt%3Bbr+%2F%26gt%3B12sqrt2%2B18%3D%5C+%3D%282-3sqrt2%29%5E2%3B%5C+x_1%3Dfrac%7B2%2B3sqrt2-2%2B3sqrt2%7D%7B2%7D%3Dfrac%7B6sqrt2%7D%7B2%7D%3D3sqrt2%3B%5C+x_2%3Dfrac%7B2%2B3sqrt2%2B2-3sqrt2%7D%7B2%7D%3Dfrac%7B4%7D%7B2%7D%3D2%3B%5C "x^2-(2+3sqrt2)x+6sqrt2=0;\ D=(2+3sqrt2)^2-24sqrt2=4+12sqrt2+18-24sqrt2=4-<br />12sqrt2+18=\ =(2-3sqrt2)^2;\ x_1=frac{2+3sqrt2-2+3sqrt2}{2}=frac{6sqrt2}{2}=3sqrt2;\ x_2=frac{2+3sqrt2+2-3sqrt2}{2}=frac{4}{2}=2;\")
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12)
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