Question

若(x+y)^2=17,(x-y)^2=3,则y/x+x/y=()

Answer 1

(x+y)^2=17,(x-y)^2=3,
∴4xy=(x+y)²-(x-y)²=17-3, x²+y²丛汪嫌=[(x+y)²+(x-y)²]/2=(17+3)/2
xy=7/陵链2, x²+y²=10
∴y/x+x/y
=(y²渗手+x²)/xy
=10/(7/2)
=20/7

Answer 2

(x+y)^2=17 -> x^2+2xy+y^2=17 (1)
(x-y)^2=3 -> x^2-2xy+y^2=3 (2)
(1)+(2) -> 2(x^2+y^2)=20 -> x^2+y^2=10
(1)-(2) -> 4xy=14 -> xy=14/4=7/2
y/粗睁孝x+x/岩稿y=(x^2+y^2)/xy=10/早明(7/2)=20/7

Answer 3

x²+2xy+y²=17①
x²-2xy+y²=3②
①答兆敬+②=2(x²+y²)=20，
x²+y²=10
①-②=4xy=14
xy=7/清慎2

y/x+x/y
=(x²+y²)/xy
=10/猜咐(7/2)
=20/7