Question

根号下x的四次方y的两次方+x的两次方y的四次方(x≥0,y≥0)

Answer 1

根号下x的四次方y的两次方+x的两次方y的四次方

=√(x^4 y²+x²y^4)

=√[x²y²(x²+y²)]

=√(x²y²)×√(x²+y²)

=xy√(x²+y²)

根号下x的3次方+3x的两次方

=√(x³+3x²)

=√[x²(x+3)]

=√x²×√(x+3)

=|x|√(x+3)

∵|x|√(x+3)=-x√(x+3)

∴x≤0 且 x+3≥0

∴x的取值范围是 -3≤x≤0