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题已知x、y∈R+满足4x+9y=1,则xy有A·最小值12B·最大值12C·最小值144D·最大值144解法1(直接利用基本不等式及不等式的性质)因为x,y∈R+,所以4x,9y∈R+,所以1=4x+9y≥24x·9y=12xy,所以xy≥12,所以xy≥144,所以选C.解法2(三角换元)因为x,y∈R+且4x+9y=1,所以可令x=cos42θ,
Known x, y ∈ R + satisfies 4x + 9y = 1, then xy has A · minimum 12B · maximum 12C · minimum 144D · maximum 144 solution 1 (direct use of the properties of the basic inequality and inequality) because x, y ∈ R +, so 4x, 9y ∈ R +, so 1 = 4x + 9 y ≥ 24x · 9y = 12xy, so xy ≥ 12, so xy ≥ 144, so choose C. solution 2 (triangle) because x, y ∈ R+ and 4x+9y=1, so x=cos42θ can be