Question

已知cosa-根号3倍的sina=4-m分之4m-6,有意义,求实数m取值范围

Answer 1

cosa-根号3倍的sina

=2sin(a+150度)

所以-2≤(4m-6)/(4-m)≤2

-2≤(4m-6)/(4-m)

-2(4-m)^2≤(4m-6)(4-m)

(4m-6+2)(4-m)≥0

(4m-6+2)(m-4)≤0

1≤m≤4

(4m-6)/(4-m)≤2

(4m-6)(4-m)≤2(4-m)^2

(4m-6-2)(4-m)≤0

(4m-8)(m-4)≥0

m≥4,m≤2

4-m在分母,m不等于4

所以1≤m≤2