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а)
![5x^4-x^2-4=0;\
t=x^2==>tgeq0==>tin[0;+infty);\
5t^2-t-4=0;\
D=(-1)^2-4cdot5cdot(-4)=1+80=81=(pm9)^2;\
t_1=frac{1-9}{2cdot5}=frac{-9}{10}=-0,9<0notin[0;+infty);\
t_2=frac{1+9}{2cdot5}=frac{10}{10}=1>0tin[0;+infty);\
x^2=1;\
x=pm1;](https://tex.z-dn.net/?f=5x%5E4-x%5E2-4%3D0%3B%5C%0At%3Dx%5E2%3D%3D%26gt%3Btgeq0%3D%3D%26gt%3Btin%5B0%3B%2Binfty%29%3B%5C%0A5t%5E2-t-4%3D0%3B%5C%0AD%3D%28-1%29%5E2-4cdot5cdot%28-4%29%3D1%2B80%3D81%3D%28pm9%29%5E2%3B%5C%0At_1%3Dfrac%7B1-9%7D%7B2cdot5%7D%3Dfrac%7B-9%7D%7B10%7D%3D-0%2C9%26lt%3B0notin%5B0%3B%2Binfty%29%3B%5C%0At_2%3Dfrac%7B1%2B9%7D%7B2cdot5%7D%3Dfrac%7B10%7D%7B10%7D%3D1%26gt%3B0tin%5B0%3B%2Binfty%29%3B%5C%0Ax%5E2%3D1%3B%5C%0Ax%3Dpm1%3B "5x^4-x^2-4=0;\
t=x^2==>tgeq0==>tin[0;+infty);\
5t^2-t-4=0;\
D=(-1)^2-4cdot5cdot(-4)=1+80=81=(pm9)^2;\
t_1=frac{1-9}{2cdot5}=frac{-9}{10}=-0,9<0notin[0;+infty);\
t_2=frac{1+9}{2cdot5}=frac{10}{10}=1>0tin[0;+infty);\
x^2=1;\
x=pm1;")
б)
![8x^6+7x^3-1=0;\
t=x^3;\
8t^2+7t-1=0;\
D=7^2-4cdot8cdot(-1)=49+82=81=(pm9)^2;\
t_1=frac{-7-9}{2cdot8}=frac{-16}{16}=-1\
t_2=frac{-7+9}{2cdot8}=frac{2}{16}=frac18\
x^3=-1==> x=-1;\
x^3=frac18;==> x=frac12;\
x=-1; frac12](https://tex.z-dn.net/?f=8x%5E6%2B7x%5E3-1%3D0%3B%5C%0A+t%3Dx%5E3%3B%5C%0A+8t%5E2%2B7t-1%3D0%3B%5C+%0AD%3D7%5E2-4cdot8cdot%28-1%29%3D49%2B82%3D81%3D%28pm9%29%5E2%3B%5C%0A+t_1%3Dfrac%7B-7-9%7D%7B2cdot8%7D%3Dfrac%7B-16%7D%7B16%7D%3D-1%5C%0A+t_2%3Dfrac%7B-7%2B9%7D%7B2cdot8%7D%3Dfrac%7B2%7D%7B16%7D%3Dfrac18%5C%0Ax%5E3%3D-1%3D%3D%26gt%3B+x%3D-1%3B%5C%0Ax%5E3%3Dfrac18%3B%3D%3D%26gt%3B+x%3Dfrac12%3B%5C%0Ax%3D-1%3B++frac12 "8x^6+7x^3-1=0;\
t=x^3;\
8t^2+7t-1=0;\
D=7^2-4cdot8cdot(-1)=49+82=81=(pm9)^2;\
t_1=frac{-7-9}{2cdot8}=frac{-16}{16}=-1\
t_2=frac{-7+9}{2cdot8}=frac{2}{16}=frac18\
x^3=-1==> x=-1;\
x^3=frac18;==> x=frac12;\
x=-1; frac12")
б)
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