a)4x²(1-x)-(1-x)=0
(1-x)(4x²-1)=0
1-x=0⇒x=1
4x²-1=0⇒4x²=1⇒x²=1/4⇒x=-1/2 U x=1/2
b)3/x(x+4)-15/x(x-4)=4/x
x(x+4)(x-4)≠0⇒x≠0,x≠-4,x≠4
3x(x-4)-15x(x+4)=4(x-4)(x+4)
3x²-12x-15x²-60x-4x²+64=0
-16x²-72x+64=0
2x²+9x-8=0
D=81+64=145
x1=(-9-√145)/4 U x2=(-9+√145)/4
2
a)(x+2)(3x-6)(2x+9)≤0
x=-2 x=2 x=-4,5
_ + _ +
---------------[-4,5]--------------[-2]------------[2]---------------------
x∈(-∞;-4,5] U [-2;2]
b)4/(x-2)-7/(x-3)≥0
(4x-12-7x+14)/(x-2)(x-3)≥0
(2-3x)/(x-2)(x-3)≥0
x=2/3 x=2 x=3
+ _ + _
-------------[2/3]------------(2)------------(3)----------------------
x∈(-∞;2/3] U (2;3)
3
4x²+3ax+1=0
D=9a²-16>0
(3a-4)(3a+4)>0
a=4/3 a=-4/3
a∈(-∞;-4/3) U (4/3;∞)