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Question

cm x^6+1 chia hết cho x^2+1

nhanh 4 ticks nhé <3

Hoàng Thanh Tuấn · Accepted Answer

$x^6+1=\left(x^2\right)^3+1^3=\left(x^2+1\right)\left(x^4-x^2+1\right)⋮\left(x^2+1\right)$

Câu trả lời:

$x^6+1=\left(x^2\right)^3+1^3=\left(x^2+1\right)\left(x^4-x^2+1\right)⋮\left(x^2+1\right)$

Đinh Đức Hùng · Answer

$x^6+1=x^6-x^2+x^2+1=x^2\left(x^4-1\right)+\left(x^2+1\right)$

$=x^2\left(x^2-1\right)\left(x^2+1\right)+\left(x^2+1\right)$

$=\left(x^2+1\right)\left[x^2\left(x^2-1\right)+1\right]⋮x^2+1$ (đpcm)

Câu trả lời:

$x^6+1=x^6-x^2+x^2+1=x^2\left(x^4-1\right)+\left(x^2+1\right)$

$=x^2\left(x^2-1\right)\left(x^2+1\right)+\left(x^2+1\right)$

$=\left(x^2+1\right)\left[x^2\left(x^2-1\right)+1\right]⋮x^2+1$ (đpcm)