若m.n(m≥0)满足3√m+5|n|=7,x=2√m=-3|n|,求x的求值范围

题目

若m.n(m≥0)满足3√m+5|n|=7,x=2√m=-3|n|,求x的求值范围

答案

m≥0
x = 2m^(1/2) >= 0,
x = -3|n| <= 0.
0 <= x <= 0
x = 0.
m = (x/2)^2 = 0
|n| = x/(-1) = 0,
n = 0.
则
3m^(1/2) + 5|n| = 0.
但这与3m^(1/2) + 5|n| = 7矛盾.
所以,x无解.
如果题目是,
若m.n(m≥0)满足3√m+5|n|=7,x=2√m=3|n|,求x的求值范围
这样的话,
x = 2√m = 3|n|,
√m = x/2,
|n| = x/3
7 = 3m^(1/2) + 5|n| = 3（x/2） + 5(x/3) = x(3/2 + 5/3) = x(19/6)
x = 6*7/19 = 42/19