nierówność kwadratowa rick: −4x²+12x>=3|2x−3|−1

M:

M:

P i P :

	3
2x−3=0 2x=3 x=
	2

	3
Dla x∊(−∞		)
	2

−4x²+12x≥3(3−2x)−1 −4x²+12x≥8−6x −4x²+18x−8≥0 4x²−18x+8≤0 Δ=196

	18−14		1
x1=		=
	8		2

	18+14
x2=		=4
	8

	1		3
x∊[		,		)
	2		2

	3
Dla x∊[		,∞)
	2

−4x²+12x≥3(2x−3)−1 −4x²+12x≥6x−10 −4x²+6x+10≥0 4x²−6x−10≤0 Δ=196

	6−14
x1=		=−1
	8

	6+14		20		5
x2=		=		=
	8		8		2

	3		5
x∊[		,		]
	2		2

	1		5
Odp. x∊[		,		]
	2		2