Question

Решите неравенство:
1) 9x^2+12x-8>4x^2+36x-24
2) 6x^2-4x-47$geq$ 8x^2+18x+2

Answer 1

1)9x^2+12x-8-4x^2-36x+24>0
5x^2-24x+16>0
5x^2-24x+16=0
D=(-24)^2-4*5*16+576-320=256=16
x1=-(-24)+16/2*5=40/10=4
x2=-(-24)-16/2*5=8/10=0,8
x<0,8
x>4
2)6x^2-4x-47-8x^2-18x-2$geq 0$
-2x^2-22x-49$geq 0$
2x^2+22x+49=0
D=22^2-4*2*49=484-392=92=9,6
x1=-22+9,6/2*2=-12,4/4=-3,1
x2=-22-9,6/2*2=-31,6/4=-7,9
-3,1$leq x leq -7,9$