Rozwiaż:
(2x-3)²-5(x+4)<(2x+1)²-2(8x+1)
(2x+3)(2x-3)-2(3x-8)>(2x-1)²
(7x-1)²-(4x-3)²≥(6x-3)²-3(ײ-2)
a) (2x-3)²-5(x+4) < (2x+1)²-2(8x+1)
(2x-3)(2x-3) -5x-20 <(2x+1)(2x+1)-16x-2
4x²-12x+9-5x-20 < 4x²+4x+1 -16x-2
-12x-5x-4x+16x < 1-2+20-9
-5x < 10 /:(-5)
x > -2
b) (2x+3)(2x-3)-2(3x-8) > (2x-1)²
4x²-9 -6x +16 > (2x-1)(2x-1)
4x² -6x + 7 > 4x²-4x +1
-6x +4x > 1-7
-2x > -6 /: (-2)
x < 3
c) (7x-1)²-(4x-3)² ≥ (6x-3)²-3(x²-2)
49x²-14x+1-(16x²-24x+9) ≥ 36x²-36x+9-3x²+6
-14x+2x+36x ≥ 9+6+9-1
24x ≥ 23/:24
x ≥ 23/24
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a) (2x-3)²-5(x+4) < (2x+1)²-2(8x+1)
(2x-3)(2x-3) -5x-20 <(2x+1)(2x+1)-16x-2
4x²-12x+9-5x-20 < 4x²+4x+1 -16x-2
-12x-5x-4x+16x < 1-2+20-9
-5x < 10 /:(-5)
x > -2
b) (2x+3)(2x-3)-2(3x-8) > (2x-1)²
4x²-9 -6x +16 > (2x-1)(2x-1)
4x² -6x + 7 > 4x²-4x +1
-6x +4x > 1-7
-2x > -6 /: (-2)
x < 3
c) (7x-1)²-(4x-3)² ≥ (6x-3)²-3(x²-2)
49x²-14x+1-(16x²-24x+9) ≥ 36x²-36x+9-3x²+6
-14x+2x+36x ≥ 9+6+9-1
24x ≥ 23/:24
x ≥ 23/24