Question

(1+x)²+3x²<(2x-1)²+7=

(x-4)²+6<x²+2x+2=

(x-1)²+7>(x+4)²=

Answer 1

a)

(1+x)²+3x²<(2x-1)²+7

1+2x+x²+3x²<4x²-4x+1+7

4x²+2x+1 < 4x²-4x +8

2x+1 < -4x +8

6x < 7

x=1⅙

 

b)

(x-4)²+6<x²+2x+2

x²-8x+16 +6 < x²+2x+2

x²-8x+22 < x²+2x+2

-8x+22 < 2x+2

-10x < -20

x > 2

 

c)

(x-1)²+7>(x+4)²

x²-2x+1+7 > x²+8x+16

x²-2x+8 > x²+8x+16

-2x+8 > 8x+16

-10x > 8

x < -⅘