证明:如果b²=ac,则(a+b+c)(a-b+c)(a²-b²+c²)=a^4+b^4+c^4.
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证明:如果b²=ac,则(a+b+c)(a-b+c)(a²-b²+c²)=a^4+b^4+c^4.
证明:如果b²=ac,则(a+b+c)(a-b+c)(a²-b²+c²)=a^4+b^4+c^4.
证明:如果b²=ac,则(a+b+c)(a-b+c)(a²-b²+c²)=a^4+b^4+c^4.
( a+b+c )( a-b+c )( a^2-b^2+c^2 )
= ( a+c+b )( a+c-b )( a^2-b^2+c^2 )
= [ ( a+c )2 - b^2 ] ( a^2-b^2+c^2 )
= ( a^2 + 2ac + c^2 - b^2 )( a^2-b^2+c^2 )
= ( a^2 + 2b^2 + c^2 - b^2 )( a^2-b^2+c^2 )
= ( a^2 + c^2 + b^2 )( a^2 + c^2 - b^2 )
= ( a^2 + c^2 )2 - (b^2)2
= a^4 + 2*a^2*c^2 + c^4 - b^4
= a^4 + 2(ac)^2 + c^4 - b^4
= a^4 + 2(b^2)^2 + c^4 - b^4
= a^4 + 2b^4 + c^4 - b^4
= a^4 + b^4 + c^4
证毕.