Question

已知a=2/(根号7+根号5),b=2/(根号7-根号5),求3*a平方-ab+3*b平方

Answer 1

a=2/(√7+√5)=2(√7-√5)/[(√7+√5)(√7-√5)]=√7-√5;

b=2/(√7-√5)=2(√7-√5)/[(√7+√5)(√7-√5)]=√7+√5;

所以：

a+b=2√7

ab=7-5=2.

3a^2-ab+3b^2

=3(a^2+b^2)-ab

=3(a^2+2ab+b^2)-7ab

=3(a+b)^2-7ab

=70.