Сумма действительных корней уравнения
([tex] x^{2} [/tex] - 10x)[tex] ^{2} [/tex] - 3 · ([tex] x^{2} [/tex] - 10x)=108 равна
([tex] x^{2} [/tex] - 10x)[tex] ^{2} [/tex] - 3 · ([tex] x^{2} [/tex] - 10x)=108 равна
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(x²-10x)²-3*(x²-10x)=108(x²-10x)=t ⇒
t²-3t-108=0 D=441
t₁=12 x²-10x=12 x²-10x-12=0 x₁=5+√37 x₂=5-√37
t₂=-9 x²-10x=-9 x²-10x+9=0 D=64 x₃=9 x₄=1.