Question

x+y=5,x²+y²=20

x和y是几

Answer 1

x+y=5,x²+y²=20
2xy = (x+y)² - (x²+y²) = 25 - 20 = 5
(x-y)² = (x²+y²) - 2xy = 20 - 5 = 15
x-y = ± 根号15
2x = ( x+y ) +( x-y ) = 5 ± 根号15
x = 2分之 ( 5 ± 根号15)

y = 2分之 ( 10 -5 ± 根号15)
= 2分之 ( 5 -+ 根号15)

追问

( 5 -+ 根号15)是什么意思？！

Answer 2

x+y=5,则y=5-x；代入x²+y²=20得
x²+(5-x)²=20
2x²-10x+25=20
2x²-10x+5=0
x=[10±√(10²-4*2*5)]/4＝(5±√15)/2