Предмет: Алгебра, автор: talylop

x^4-101x^2+100=0

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Ответы

Автор ответа: sangers1959
1

Объяснение:

x^4-101x^2+100=0\\

Пусть х²=t≥0   ⇒    

t^2-101t+100=0\\D=9801;\sqrt{D}=99\\ t_1=x^2=100\\x^2-100=0\\x^2-10^2=0\\(x+10)(x-10)=0\\x_1=-10;x_2=10\\t_2=x^2=1\\x^2-1=0\\(x+1)(x-1)=0\\x_3=-1;x_4=1.

Ответ: x₁=-10, x₂=10, x₃=-1, x₄=1.

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