Question

已知x+y=4,xy=1求x五次方y四次方+x四次方y五次方

2.因式分解（a-b）²-16（a+b）²3.先化简，再求值：已知x+y=2，xy=四分之三，求x³y+xy³+2x²y²

Answer 1

x的5次方y的4次方+x的4次方y的5次方
=x的4次方y的4次方(x+y)
=(xy)的4次方(x+y)
=1的4次方×4
=1×4
=4

(a-b)²-16(a+b)²
=[(a-b)+4(a+b)][(a-b)-4(a+b)]
=(5a+3b)(-3a-5b)
=-(5a+3b)(3a+5b)

x³y+xy³+2x²y²
=xy(x²+2xy+y²)
=xy(x+y)²
=4分之3×2²
=4分之3×4
=3

Answer 2

x五次方y四次方+x四次方y五次方
=x四次方y四次方（x+y）
=（xy）四次方（x+y）
=1的四次方×4
=4

（a-b）²-16（a+b）²
=（a-b）²-（4a+4b）²
=（a-b+4a+4b）（a-b-4a-4b）
= -（5a+3b）（3a+5b）

x³y+xy³+2x²y²
=xy(x²+y²+2xy)
=xy(x+y)²
=(3/4)×2²
=3

Answer 3

解
x+y=4
xy=1
x^5y^4+x^4y^5
=(xy)^4(x+y)
=1×4
=4

(a-b)²-16(a+b)²是这个吗
=[(a-b)-4(a+b)][(a-b)+4(a+b)]
=(-3a-5b)(5a+3b)
=-(3a+5b)(5a+3b)

x³y+xy³+2x²y²
=xy(x²+2xy+y²)
=xy(x+y)²
=3/4×4
=3

Answer 4

x^5y^4+x^4y^5
=x^4y^4(x+y)=1×4=4
(2)（a-b）²-16（a+b）²
=[(a-b)+4(a+b)][(a-b)-4(a+b)]
=-(5a+3b)(3a+5b)
(3)x³y+xy³+2x²y²
=xy(x²+y²+2xy)
=xy(x+y)²
∵x+y=2,xy=3/4
∴上式=3/4×2²=3