已知0≤x≤π/2求使根号3sinx+cosx=4m-6/4-m有意义的实数m的取值范围
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0≤x≤π/2
√3sinx+cosx = (4m-6)/(4-m)
2(sinxcosπ/3+cosxsinπ/3) = (4m-6)/(4-m)
sin(x+π/3) = (2m-3)/(4-m)
-1≤(2m-3)/(4-m)≤1
(2m-3)/(4-m)+1≥0，并且(2m-3)/(4-m)-1≤0
(m+1)/(4-m)≥0，并且(3m-7)/(4-m)≤0
(m+1)/(m-4)≤0，并且(3m-7)/(m-4)≥0
-1≤m＜4；并且m≤7/3，或m＞4
∴-1≤m≤7/3
√3sinx+cosx = (4m-6)/(4-m)
2(sinxcosπ/3+cosxsinπ/3) = (4m-6)/(4-m)
sin(x+π/3) = (2m-3)/(4-m)
-1≤(2m-3)/(4-m)≤1
(2m-3)/(4-m)+1≥0，并且(2m-3)/(4-m)-1≤0
(m+1)/(4-m)≥0，并且(3m-7)/(4-m)≤0
(m+1)/(m-4)≤0，并且(3m-7)/(m-4)≥0
-1≤m＜4；并且m≤7/3，或m＞4
∴-1≤m≤7/3
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