Question

已知x等于根号5加2，y等于根号5减2，求下列各式的值： 〔1〕xy平方加x平方y； 〔2〕x平方减xy加y平方

Answer 1

1,
xy平方加x平方y
=xy²+x²y
=xy(y+x)
=(根号5+2)(根号5-2)(根号5-2+根号5+2)
=[(根号5)²-2²](2*根号5)
=[5-4](2*根号5)
=2*根号5;

2,
x平方减xy加y平方
=x²-xy+y²
=x²-xy-xy+y²+xy
=(x-y)²+xy
=(根号5-2+根号5+2)²+(根号5+2)(根号5-2)
=(2*根号5)²+[(根号5)²-2²]
=20+5-4
=21

Answer 2

xy=5-4=1,xy平方加x平方y=xy(y+x)=2根号5;x平方减xy加y平方=(x-y)^2+xy=17

Answer 3

xy^2+x^2y=xy(x+y)=2根号5
x平方减xy加y平方=9+4根号5-1+9-4根号5=17

Answer 4

解:x=√5+2; y=√5-2.
则：x+y=2√5; xy=(√5+2)*(√5-2)=1.
(1)xy²+x²y=xy(y+x)=1*(2√5)=2√5;
(2)x²-xy+y²=(x+y)²-3xy=(2√5)²-3*1=20-3=17.

Answer 5

【1】xy²+x²y=xy(x+y)=(√5+2)(√5-2)(2√5)=(5-4)(2√5)=2√5
【2】x²-xy+y²＝(x-y)²+xy=4²+(√5+2)(√5-2)=16+(5-4)=17

Answer 6

〔1〕xy²＋x²y
=xy(x＋y)
=(√5＋2)(√5－2)(√5＋2＋√5－2)
=(5－4)(2√5)
=2√5
〔2〕x²－xy＋y²
=(x－y)²＋xy
=[√5＋2－(√5－2)]²＋(√5＋2)(√5－2)
=4²＋√5²－2²
=16＋5－4
=17