a+b=5,ab=4,(√a-√b)/(√a+√b)=?

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a+b=5,ab=4,(√a-√b)/(√a+√b)=?
a+b=5,ab=4,(√a-√b)/(√a+√b)=?

a+b=5,ab=4,(√a-√b)/(√a+√b)=?
(a+b)²=5²
a²+2ab+b²=25
a²+b²=25-2ab=17
(a-b)²
=a²-2ab+b²
=17-8
=9
所以a-b=±3
上下乘√a+√b
原式=(√a-√b)(√a+√b)/(√a+√b)²
=(a-b)/(a+b+2√ab)
=±3/(5+4)
=±1/3

.(√ a-√ b)÷(√ a+√ b)=(√ a-√ b)^2/(√ a-√ b)(√ a+√ b))=(a+b-2√ ab)/a-b=-1/3或1/3
又因为(a-b)^2=(a+b)^2-4ab=9 a-b=3或 a-b=-3

(√a-√b)/(√a+√b)
=(√a-√b)^2/[(√a+√b)*(√a-√b)]
=[a-2√(ab)+b]/(a-b)
=(5-2*2)/[a+b-4√(ab)]
=1/(-3)
= -1/3