Question

已知x+2y=5,xy=1求2x^2y+4xy^2求1-二分之一x^2y-xy^2求(x^2+1)(4y^2+1)

Answer 1

2x^2y+4xy^2=2xy(x+2y)=2*1*5=10

1-二分之一x^2y-xy^2=1-(1/2)xy(x+2y)=1-5/2=-3/2

x+2y=5,xy=1

(x+2y)²=x²+4y²+4xy=25

x²+4y²=25-4xy=25-4=21

(x^2+1)(4y^2+1)

=4x²y²+x²+4y²+1

=4(xy)²+21+1

=4+21+1

=26