计算:(1) 1/(√2)-1/(√3)-1/(√2-√3) (2) 如果a=4+√3,b=13/(4+√3)
问题描述:
计算:(1) 1/(√2)-1/(√3)-1/(√2-√3) (2) 如果a=4+√3,b=13/(4+√3)
求a/(a-根号下ab)-√b/(√a+√b)的值.
答
:(1) 1/(√2)-1/(√3)-1/(√2-√3)
=√2/2-√3/3+√3-√2
=2√3/3-√2/2.
(2) a=4+√3,b=13/(4+√3)=4-√3,
∴a+b=8,a-b=2√3,
∴a/[a-√(ab)]-√b/(√a+√b)
=√a/(√a-√b)-√b/(√a+√b)
=[√a(√a+√b)-√b(√a-√b)]/(a-b)
=(a+b)/(a-b)
=4√3/3.