证明a−1a−1+b−1+a−1a−1−b−1=2b2b2−a2
已知:(a−1a−1+b−1+a−1a−1−b−1=2b2b2−a2)
要求:证明 L.H.S.=R.H.S.
解答: 给定表达式:a−1a−1+b−1+a−1a−1−b−1
L.H.S.=1a1a+1b+1a1a−1b
=1aa+bab+1ab−aab
=aba(a+b)+aba(b−a)
=bb+a+bb−a
=b(b−a)+b(b+a)(b+a)(b−a)
=b2−ab+b2+abb2−a2
=2b2b2−a2
=R.H.S.
因此,证明了 (a−1a−1+b−1+a−1a−1−b−1=2b2b2−a2)
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