因式分解x^4-6x^2+1

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因式分解x^4-6x^2+1因式分解x^4-6x^2+1因式分解x^4-6x^2+1x^4-6x"+1=(x")"-2x"+1-4x"=(x"-1)"-(2x)"=(x"-2x-1)(x"+2x-1)

因式分解x^4-6x^2+1
因式分解x^4-6x^2+1

因式分解x^4-6x^2+1

x^4 - 6x" + 1
= ( x" )" - 2x" + 1 - 4x"
= ( x" - 1 )" - ( 2x )"
= ( x" - 2x - 1 )( x" + 2x - 1 )
= ( x" - 2x + 1 - 2 )( x" + 2x + 1 - 2 )
= [ ( x - 1 )" - ( √2 )" ][ ( x + 1 )" - (...

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x^4 - 6x" + 1
= ( x" )" - 2x" + 1 - 4x"
= ( x" - 1 )" - ( 2x )"
= ( x" - 2x - 1 )( x" + 2x - 1 )
= ( x" - 2x + 1 - 2 )( x" + 2x + 1 - 2 )
= [ ( x - 1 )" - ( √2 )" ][ ( x + 1 )" - ( √2 )" ]
= ( x - 1 - √2 )( x - 1 + √2 )( x + 1 - √2 )( x + 1 + √2 )

其实,减少根号也完全有办法,
或许,被采纳的答案反而不对,
看一看,他的根号里面,也都是完全平方嘛,
3 + 2√2
= 2 + 2√2 + 1
= (√2)" + 2√2 + 1"
= ( √2 + 1 )"

3 - 2√2
= 2 - 2√2 + 1
= (√2)" - 2√2 + 1"
= ( √2 - 1 )"

当然,他这样配方
也的确是另一个方案

= ( x" )" - 6x" + 3" - 9 + 1
= ( x" - 3 )" - 8
= ( x" - 3 - 2√2 )( x" - 3 + 2√2 )
= [ x" - ( 3 + 2√2 ) ][ x" - ( 3 - 2√2 ) ]

可是我们就要看出,
括号里其实就是完全平方,
也就不需要加根号了

= [ x" - ( 2 + 2√2 + 1 ) ][ x" - ( 2 - 2√2 + 1 ) ]
= [ x" - ( √2 + 1 )" ][ x" - ( √2 - 1 )" ]
= [ x + ( √2 + 1 ) ][ x - ( √2 + 1 ) ][ x + ( √2 - 1 ) ][ x - ( √2 - 1 ) ]
= ( x + √2 + 1 )( x - √2 - 1 )( x + √2 - 1 )( x - √2 + 1 )

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