Question

已知a=√2+1,b=﹙√2+1﹚分之1,求﹙2a+2b﹚分之a的平方减b的平方

Answer 1

∵b=1/(√2+1)

=(√2-1)/[(√2+1)(√2-1)]

=(√2-1)/(2-1)

=(√2-1)

∴(a²-b²)/(2a+2b)

=(a+b)(a-b)/[2(a+b)]

=(a-b)/2

=[(√2+1)-(√2-1)]/2

=2/2

=1

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