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scorpion228
@scorpion228
July 2022
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решите с помощью теоремы Виета и найдите x1, x2: x^2-10x+9=0, x^4+5x^2-36, x^4-10x^2+9=0
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Alexandr130398
Теорема Виета: x²+bx+c=0
x₁+x₂=-b
x₁*x₂=c
1)x²-10x+9=0
x₁=9: х₂=1
2)x⁴+5x²-36=0, пусть х²=t, тогда
t²+5t-36=0
t₁=-9; t₂=4
x²=4;
x₁=2
x₂=-2
3)x⁴-10x²+9=0
t²-10t+9=0
t₁=9; t₂=1
x²=9;x²=1
x₁=3;x₂=-3;x₃=1;x₄=-1
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Answers & Comments
x₁+x₂=-b
x₁*x₂=c
1)x²-10x+9=0
x₁=9: х₂=1
2)x⁴+5x²-36=0, пусть х²=t, тогда
t²+5t-36=0
t₁=-9; t₂=4
x²=4;
x₁=2
x₂=-2
3)x⁴-10x²+9=0
t²-10t+9=0
t₁=9; t₂=1
x²=9;x²=1
x₁=3;x₂=-3;x₃=1;x₄=-1