Question

若a平方+b平方=3ab,求分式[1+(a平方-b平方分之2b平方)][1+(a-b分之2b)]的值

Answer 1

(a-b)²=a²+b²-2ab=3ab-2ab=ab

[1 + 2b²/(a²-b²)] [1 + 2b/(a-b)]

= [(a²-b²+2b²)/(a²-b²)] [(a-b+2b)/(a-b)] (通分)

= [(a²+b²)/(a²-b²)] [(a+b)/(a-b)]

= [(a²+b²)/(a-b)(a+b)] [(a+b)/(a-b)]

=(a²+b²)/(a-b)²

=3ab/ab

=3