Question

已知x等于根号6减去根号5除以根号6加上根号5,y等于根号6加上根号5除以根号6减去根号5,求y/x-x/y的值

Answer 1

x等于根号6减去根号5除以根号6加上根号5

x=√6-√5/√6+√5

x=(√6-√5)^2/(√6+√5)(√6-√5)

x=(√6-√5)^2

y等于根号6加上根号5除以根号6减去根号5

y=√6+√5/√6-√5

y=(√6+√5)^2/(√6+√5)(√6-√5)

y=(√6+√5)^2

y/x-x/y

=y^2-x^2/xy

=(√6+√5)^4-(√6-√5)^4/(√6-√5)^2(√6+√5)^2

=((√6+√5)^2+(√6-√5)^2)((√6+√5)^2+(√6-√5)^2)/((√6-√5)(√6+√5))^2

=(6+2√30+5+6-2√30+5)(6+2√30+5-6+2√30-5)/(6-5)^2

=22* 4√30

=88√30